Question

Set up, but do not evaluate, an integral for the area of the resulting surface when the given curve is rotated about the y-axis. (a) Integrate with respect to x. (b) Integrate with respect to y.

Answer 1

To set up the integral for the area of the resulting surface when the curve is rotated about the y-axis, we need to determine the limits of integration and the integrand.

Step-by-step explanation:

To set up the integral for the area of the resulting surface when the curve is rotated about the y-axis, we need to determine the limits of integration and the integrand.

(a) Integrate with respect to x: To do this, we need to express the curve in terms of x and determine the limits of integration in terms of x. Then, the integral will be ∫[f(x) - g(x)] dx, where f(x) and g(x) are the upper and lower limits of the curve, respectively.

(b) Integrate with respect to y: To do this, we need to express the curve in terms of y and determine the limits of integration in terms of y. Then, the integral will be ∫[h(y) - k(y)] dy, where h(y) and k(y) are the right and left limits of the curve, respectively.