Find the volume of the solid, generated by revolving the region bounded by y=sqrt(sin(4x)), y=0 and 0 leq x leq pi/4 about the x-axis.

Liam Potter 2022-09-16 Answered
Finding Volume of object in 3D space rotating on x-axis
Find the volume of the solid, generated by revolving the region bounded by y = sin ( 4 x ) , y = 0 and 0 x π 4 about the x-axis.
To solve for volume, I have the following integral
V = 0 π / 4 π r ( x ) 2 d x = π 0 π / 4 sin ( 4 x ) d x = π [ cos ( 4 x ) 4 ] 0 π / 4 = π 4 .
That is not one of the solution options. What did I do wrong?
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Answers (2)

Alec Reid
Answered 2022-09-17 Author has 9 answers
Explanation:
If you evaluate π [ 1 / 4 cos ( 4 x ) ] 0 π / 4 = π / 4 ( 1 1 ) = π / 2

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Heergerneuu
Answered 2022-09-18 Author has 2 answers
Explanation:
V = π 0 π / 4 r ( x ) 2 d x = π 0 π / 4 sin ( 4 x ) d x = π 4 cos ( 4 x ) | 0 π / 4 = π 4 [ 1 1 ] = π 2

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