The graph of a function is shown below as a blue curve. Create a visualization of a midpoint approximation for the area under the curve on the interval [1, 7] using 5 rectangles. Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown. Finally, drag the black movable points to adjust the height of each of the rectangular boxes.
The graph of a function is shown below as a blue curve. Create a visualization of a left-endpoint approximation for the area under the curve on the interval [-4, 3] using 6 rectangles. Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown. Finally, drag the black movable points to adjust the height of each of the rectangular boxes. Provide your answer below:
The graph of a function is shown below as a blue curve. Create a visualization of a right-endpoint approximation for the area under the curve on the interval [-6, -2] using 6 rectangles. Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown. Finally, drag the black movable points to adjust the height of each of the rectangular boxes. Provide your answer below:
The graph of a function is shown below as a blue curve, Create a visualization of a left-endpoint approximation for the area under the curve on the interval [-1, 2] using 4 rectangles: Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown, Finally, drag the black movable points to adjust the height of each of the rectangular boxes. Provide your answer below:
The graph of a function is shown below as a blue curve. Create a visualization of a midpoint approximation for the area under the curve on the interval [-1, 2] using 3 rectangles. Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown. Finally, drag the black movable points to adjust the height of each of the rectangular boxes. Provide your answer below:
The graph of a function is shown below as a blue curve. Create a visualization of a midpoint approximation for the area under the curve on the interval [-1, 4] using 6 rectangles. Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown. Finally, drag the black movable points to adjust the height of each of the rectangular boxes. Provide your answer below:
The graph of a function is shown below as a blue curve. Create a visualization of a left-endpoint approximation for the area under the curve on the interval [1, 7] using 8 rectangles. Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown. Finally, drag the black movable points to adjust the height of each of the rectangular boxes. Provide your answer below:
The graph of a function is shown below as a blue curve. Create a visualization of a left-endpoint approximation for the area under the curve on the interval [-6, 3] using 9 rectangles. Slide the orange points horizontally to adjust the endpoints of the interval. Use the vertical slider on the right side of the graphing window (blue movable point) to control how many rectangles your approximation for the area will have. The value of each rectangle’s width, ∆x, is also shown. Finally, drag the black movable points to adjust the height of each of the rectangular boxes. Provide your answer below:
Given the graph of the function f(x) below, approximate the area under the curve over the interval [1, 6] using a trapezoidal approximation with 5 trapezoids. Submit an exact answer.
Use the trapezoidal rule to approximate the area under the curve f(x) = 3x^2/x+2 on the interval [0, 4]. Use n = 4. Submit an exact answer.
Calculate the absolute error in the estimate of ∫-2 2 (2 - 2x/5) dx using the midpoint rule with n = 2. Enter answer using exact values.
Calculate the relative error in the estimate of ∫1 5 (2x^2 - x)dx using the Trapezoid rule with n = 4. Round your answer to the nearest hundredth as necessary.
Find the upper bound for the error using the midpoint rule with n = 5 subintervals. ∫ 3π -3π (sin(x) + cos(x))dx Round your answer to the nearest hundredth as necessary.
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use the midpoint rule? ∫ 4 1 (5x^2 + 2x + 1)dx
Calculate the relative error in the estimate of ∫1 5 (4x^2 - x)dx using the Trapezoid rule with n = 2. Round your answer to the nearest hundredth as necessary.
Calculate the relative error in the estimate of ∫1 5 (4x^2 - x)dx using the Trapezoid rule with n = 4. Round your answer to the nearest hundredth as necessary.
Calculate the relative error in the estimate of ∫-6 -3 (x^2/5) dx using the midpoint rule with n = 3. Round your answer to the nearest hundredth as necessary.
Calculate the relative error in the estimate of ∫-6 -3 (x^2/5) dx using the midpoint rule with n = 3. Round your answer to the nearest hundredth as necessary.
Calculate the absolute error in the estimate of ∫1 5 (4x^2 - x)dx using the Trapezoid rule with n = 4. Enter answer using exact values.
Calculate the relative error in the estimate of ∫-2 4 (x^2/2) dx using the midpoint rule with n = 3. Round your answer to the nearest hundredth as necessary.
Calculate the absolute error in the estimate of ∫1 -1 (4x^2 - x)dx using the Trapezoid rule with n = 1. Round your answer to the nearest hundredth as necessary.
Find the upper bound for the error using the midpoint rule with n = 3 subintervals. ∫ 3 0 (4x^3)dx Round your answer to the nearest hundredth as necessary.
Find the upper bound for the error using the midpoint rule with n = 3 subintervals. ∫ 3π π (sin(x))dx Round your answer to the nearest hundredth as necessary.
Find the upper bound for the error using the midpoint rule with n = 6 subintervals. ∫ 4π -2π (cos(x))dx Round your answer to the nearest hundredth as necessary.
Find the upper bound for the error using the midpoint rule with n = 5 subintervals. ∫ 3π -2π (sin(x) + cos(x))dx Round your answer to the nearest hundredth as necessary.
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use the trapezoid rule? ∫ 2 0 (e x^2 )dx
Find the upper bound for the error using the Trapezoid rule with n = 2 subintervals. ∫ 1 -2 (2e^2x)dx Round your answer to the nearest hundredth as necessary.
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use trapezoid rule? ∫ 1 0 (2e^x)dx
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use the trapezoid rule? ∫ 1 -1 (e 2x^2 )dx
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use Simpson's rule? ∫ 2 -2 (2e^x)dx
Use Simpson’s rule with 2 subintervals to estimate ∫0 2 f(x)dx given the graph of f(x) below. Enter your answer as an exact answer.
Use Simpson’s rule with 2 subintervals to estimate ∫1 5 f(x)dx given the table of f(x) below. x f(x) 1 6 2 13 3 26 4 45 5 70 Enter your answer as an exact answer.
Calculate the absolute error in the estimate of ∫1 5 (2x^4 - 3x^2)dx using Simpson's rule with n = 4. Enter an exact value.
Use Simpson’s rule with 2 subintervals to estimate ∫0 2 f(x)dx given the graph of f(x) below. Enter your answer as an exact answer.
Use Simpson’s rule with 4 subintervals to estimate ∫0 4 f(x)dx given the graph of f(x) below. Enter your answer as an exact answer.
Use Simpson’s rule with 4 subintervals to estimate ∫2 6 (3x^2 - 2x + 4)dx. Enter your answer as an exact answer
Find the upper bound for the error in estimating the integral below using Simpson's rule with n = 6 subintervals. ∫ 1 -2 (e^2x)dx Round your answer up to the nearest hundredth.
Find the upper bound for the error in estimating the integral below using Simpson's rule with n = 2 subintervals. ∫ 1 -2 (2e^2x)dx Round your answer up to the nearest hundredth.
Find the upper bound for the error in estimating the integral below using Simpson’s rule with n = 2 subintervals. ∫ 0 1 (e^2x)dx Round your answer to the nearest hundredth as necessary.
Find the upper bound for the error in estimating the integral below using Simpson's rule with n = 4 subintervals. ∫ 1 -2 (2e^2x )dx Round your answer up to the nearest hundredth.
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use Simpson's rule? ∫ 1 -2 (2e^x)dx
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use Simpson's rule? ∫ 2 -1 (2e 2x^2)dx
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use Simpson's rule? ∫ 2 1 (4x^5 + 2x^2 + 2x)dx
What is the minimum value of n that will guarantee the estimate of the integral below is accurate to within 0.01 if we use Simpson's rule? ∫ 3 1 (2x^5 – x^2 + 2x)dx
Calculate the relative error in the estimate of ∫2 6 (2x^4 - 3x^2)dx using Simpson's rule with n = 2. Round your answer to the nearest hundredth.
Evaluate the integral. ∫ 4 -∞ -5 / x^2 + 16 dx If the integral is divergent, enter ∅. If the integral is convergent, enter your answer using exact values in terms of π.
Evaluate the integral. ∫ ∞ -3 e^-2xdx If the integral is divergent, enter ∅. If the integral is convergent, enter your answer using exact values.
Evaluate the integral. ∫ 4 0 xln(3x)/4 dx Give an exact answer. If the integral is divergent, enter ∅.
Evaluate the integral. ∫ π/2 3π/8 2sec^2(4x)dx If the integral is divergent, enter ∅.
Determine whether the Comparison Test will prove whether the integral ∫0 ∞ sin2 (x)+2 √x 3 +9 dx converges or diverges by comparing it to the integral ∫0 ∞ 3 √x 3 +9 dx, or if it will be inconclusive. C converges Diverges Inconclusive
Determine whether the Comparison Test will prove whether the integral ∫1 ∞ ln(x)+5 3x+8 dx converges or diverges by comparing it to the integral ∫1 ∞ 1 x+8 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫1 ∞ ln(x)+2 √x 3 +2 dx converges or diverges by comparing it to the integral ∫1 ∞ 1 √x 3 +2 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫1 ∞ ln(x)+3/x^2+8 dx converges or diverges by comparing it to the integral ∫1 ∞ 1/x^2+8 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫0 ∞ sin2 (x)+1 x^2+4 dx converges or diverges by comparing it to the integral ∫0 ∞ 2 x^2+4 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫0 ∞ sin2 (x)+2/x+5 dx converges or diverges by comparing it to the integral ∫0 ∞ 3/x+5 dx, or if it will be inconclusive.
Determine whether the integral g(x) = ∫8 ∞ sin2 (x)+4 √x+2 dx diverges by comparing it to the integral f(x) = ∫8 +∞ 3 √x+2 dx.
Determine whether the Comparison Test will prove whether the integral ∫0 ∞ sin2 (x)+4 √x 3 +5 dx converges or diverges by comparing it to the integral ∫0 ∞ 5 √x 3 +5 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫0 ∞ sin2 (x)+1 √x 3 +8 dx converges or diverges by comparing it to the integral ∫0 ∞ 2 √x 3 +8 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫1 ∞ 3/3x^4+2 dx converges or diverges by comparing it to the integral ∫1 ∞ 1/x^4 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫-∞ 1 1+e^-2x x^2+2 dx converges or diverges by comparing it to the integral ∫-∞ 1 1 x^2+2 dx, or if it will be inconclusive.
On the graph below, we have three functions f(x) = 1/x^2 , g(x) = 7/x^2+2 , and h(x) = e^-x . If, on the interval [3, ∞), we know that ∫ ∞ 3 1 x2 dx converges and h(x) ≤ f(x) ≤ g(x), which of the following statements are true? ∫ ∞ 3 g(x)dx diverges ∫ ∞ 3 h(x)dx diverges ∫ ∞ 3 g(x)dx converges ∫ √ 3 3 h(x)dx converges
Determine whether the Comparison Test will prove whether the integral ∫5 ∞ 2 4 √x 3 +2 dx converges or diverges by comparing it to the integral ∫5 ∞ 1 √x 3 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫7 ∞ 1/2x^2+5 dx converges or diverges by comparing it to the integral ∫7 ∞ 1/x^2 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫6 ∞ 4/3x^2+1 dx converges or diverges by comparing it to the integral ∫6 ∞ 1/x^2 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫1 ∞ 1/√x+5 dx converges or diverges by comparing it to the integral ∫1 ∞ 1/√x dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫1 ∞ 1/3x^2+1 dx converges or diverges by comparing it to the integral ∫1 ∞ 1/x^2 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫-∞ 1 1+e^-2x/x^2+2 dx converges or diverges by comparing it to the integral ∫-∞ 1 1/x^2+2 dx, or if it will be inconclusive.
On the graph below, we have three functions f(x) = 1/x^2 , g(x) = 7/3x^2+1 , and h(x) = e^-x . If, on the interval [3, ∞), we know that ∫ ∞ 3 1 x2 dx converges and h(x) ≤ f(x) ≤ g(x), which of the following statements are true? ∫ ∞ 3 g(x)dx diverges ∫ ∞ 3 h(x)dx diverges ∫ ∞ 3 g(x)dx converges ∫ √ 3 3 h(x)dx converges
Determine whether the Comparison Test will prove whether the integral ∫2 ∞ 6/2x^3+4 dx converges or diverges by comparing it to the integral ∫2 ∞ 1/x^3 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫3 ∞ e^3x+3/x+6 dx converges or diverges by comparing it to the integral ∫3 ∞ 1/x+6 dx, or if it will be inconclusive.
On the graph below, we have three functions f(x) = 1/x^2 , g(x) = 7/x^2+2 , and h(x) = e^-x . If, on the interval [2, ∞), we know that ∫ ∞ 2 1 x2 dx converges and h(x) ≤ f(x) ≤ g(x), which of the following statements are true? ∫ ∞ 2 g(x)dx diverges ∫ ∞ 2 h(x)dx diverges ∫ ∞ 2 g(x)dx converges ∫ ∞ 2 h(x)dx converges
Determine whether the Comparison Test will prove whether the integral ∫5 ∞ 2 4 √x 3 +2 dx converges or diverges by comparing it to the integral ∫5 ∞ 1 √x 3 dx, or if it will be inconclusive.
Determine whether the Comparison Test will prove whether the integral ∫1 ∞ 3/4x^4+5 dx converges or diverges by comparing it to the integral ∫1 ∞ 1/x^4 dx, or if it will be inconclusive.