Find the volume of the solid obtained by rotating the region enclosed by the graphs y = 4/x, y = 5, and y = 9, x ≥ 0 about the y axis, as shown in the figure. (Use symbolic notation and fractions where needed.) V =
Let S be the region bounded by y − x = −4, y−x = 0, 3 y+x = 4 and 3y+x = 12. Use a linear transformation to transform S into a rectangular region and evaluate the integral ∬S20(y − x)2(3y + x) dAxy (It may help to sketch the region on the uv-axis)
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = 5/x, y = 5/x2, x = 3 Find the area of the region.
