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  • Math Archive: Questions from 2024-01-2

    R is the region bounded by the functions f(x) = 1 - 3sin(x) and g(x) = 3cos(x). Find the area of the region bounded by the functions on the interval [0, π/2]. Enter an exact answer.

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    R is the region bounded above by the function f(x) = x + 10 and below by the function g(x) = x/4 + 2 over the interval [a, b] where a = -6 and b = -2. Represent the area A of R by writing an integral with respect to x. You do not need to simplify.

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    R is the region bounded by the functions f(x) = √5x - 7 and g(x) = x – 3/5. Find the area A of R. Enter an exact answer.

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    R is the region bounded by the functions f(x) = 3e^x - 2 and g(x) = x^2 - 2. Find the area of the region bounded by the functions on the interval [-1, 1]. Enter an exact answer.

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    R is the region bounded by the functions f(x) = -2x^2 + 8x - 3 and g(x) = -2x + 5. Find the area A of R. Enter an exact answer.

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    R is the region bounded by the functions f(x) = -x^2 - x + 5 and g(x) = -1. Find the area A of R. Enter an exact answer.

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    R is the region bounded by the functions f(x) = 2x^2 + 4x - 5 and g(x) = 1. Find the area A of R. Enter answer using exact values.

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    R is the region bounded by the functions f(x) = 3x^2 + 27x + 54 and g(x) = -3x^2/2 - 27x^2 - 27. Find the area A of R. Enter an exact answer.

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    R is the region bounded by the functions f(x) = 5x/3 + 2 and g(x) = -2x + 5 over the interval [a, b] where a = 1 and b = 4. Represent the area A of R by writing an integral with respect to x. You do not need to simplify.

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    R is the region bounded by the functions f(x) = -x/2 - 6 and g(x) = 9x/4 - 3 over the interval [a, b] where a = -1 and b = 3. Represent the area A of R by writing an integral with respect to x. You do not need to simplify.

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    R is the region bounded by the functions f(x) = 4√x and g(x) = 4x/3 + 8/3. Find the area A of R. Enter an exact answer.

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