MAT136H1 Lecture : 8.2 Surface Area of Revolution Question #3 (Medium)

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #3 (medium): surface area from rotating the function about the y-axis. When the function is rotated about the -axis, the radius extends horizontally. When the function is expressed as , then ( can be used. But if the function is given in the form of , then ( is used. The expression that comes from arc length can be evaluated with just as well because ( The function does not have to be rearranged, but the derivative can be taken as it is. Find the exact surface area obtained by rotating the given function about the -axis. Since the rotation is about the y-axis, ( is used. Taking the derivative of x with respect to y: Since it follows after chain rule, substitution can be used.