# (solution) Consider the following: x = 4 times the square root of sin(y); 0

Consider the following:

x = 4 times the square root of sin(y);  0 ? y ? ?;  x = 0;  about y = 4

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve around the specified axis.

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? ( ) ,0 ? =4
? ( ) ,0 ? =4
( ?
? ) =0 ? =4 ? =0
= ( ) ?
( ) ? =4
? ? 0?
= ( )
? ? .
? 0? 0? ?4 2 =4 ( ) =&gt; = 16 =&gt; ( )= ( )
16 . ?4
0? ? 2…