MAT136H1 Lecture : 8.2 Surface Area of Revolution Question #1 (Easy)

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

Document Summary

Question #1 (easy): finding the surface area from rotating the function about the x-axis. When the function is rotated about the -axis, then the radius extends vertically up. When the function is expressed as , then use the formula ( form of , then use ( But if the function is given in the. The part that comes from arc length can be evaluated with because based on ( So other than rearrangement of the function is needed to express the vertically stretching radius, but as for the ds portion, the derivative can be taken as it is. Find the exact surface area obtained by rotating the given function about the -axis. From comes the integral expression for the surface area from rotating the function about the x-axis: Notice it incorporates the formula for arc length. Plugging into the sa equation: substitution can be used. let , then and.