How do you find the volume of the region enclosed

Hayley Sanders

Hayley Sanders

Answered question

2022-05-21

How do you find the volume of the region enclosed by the curves y=x, y=-x, and x=1 rotated about y=1?

Answer & Explanation

Erzrivalef6

Erzrivalef6

Beginner2022-05-22Added 10 answers

Explanation:
Using the method of washers
Let the outer radius be 1-(-x)=1+x
Let the inner radius be 1-x
The integral for the volume is
π 0 1 ( 1 + x ) 2 ( 1 x ) 2 d x
π 0 1 ( 1 + 2 x + x 2 ) ( 1 2 x + x 2 ) d x
π 0 1 ( 1 + 2 x + x 2 1 + 2 x x 2 ) d x
π 0 1 ( 4 x ) d x
Integrating we get
2 π x 2
Evaluating from 0 to 1
2 π ( 1 ) 2 0 = 2 π

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