Question

How do you find the area of the surface generated by rotating the curve about the y-axis `x=2t+1, y=4-t, 0<=t<=4`?

Answer 1

First we will combine this 2 equation to find x in term of y and then we will calculate the area.

Explanation:

`y=4-t iff t=4-y`
we plug this value into `x=2t+1 iff x=2(4-y)+1 iff x=9-2y`
this gives us the curve
graph{x=9-2y [-10, 10, -5, 5]}
and `0<=y<=4`
the area generated is given by the integral:
`E=int_0^4(9-2y)dy`
because we rotate the curve about the y-axis
so `E=[9y-y^2]_0^4=36-16=20`