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#?

1 Answer
Jul 17, 2017

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#