Thread: Find the area

Find the exact area of the surface obtained by rotating the given curves around the x-axis.

x = 3t - t^2, y = 3t^2, 0 <= t <= 1

My work:

2pi * Integral from 0 to 1 of 3t^2 root[ ( 3-2t)^2 + (6t)^2)] dt

2pi Int 0-->1 of 3t^2 root[ 40t^2 - 12t + 9]dt

This can't be right...

Originally Posted by veronicak5678

Find the exact area of the surface obtained by rotating the given curves around the x-axis.

x = 3t - t^2, y = 3t^2, 0 <= t <= 1

My work:

2pi * Integral from 0 to 1 of 3t^2 root[ ( 3-2t)^2 + (6t)^2)] dt

2pi Int 0-->1 of 3t^2 root[ 40t^2 - 12t + 9]dt

This can't be right...

I agree, recheck the problem statement. As it stands, the exact solution is one ugly ...

I wrote to my professor and he told me it was a typo. It was supposed to be 3t - t^3. I was going to delete this post but I don't know how! Thanks for your help.