We consider the plane region R delimited by the curves y = cos (x) and y = (x − π) ^ 2 −2.
(a) Determine the volume of the solid generated by the rotation of R revolves around the right y = −3. (b) Determine the volume of the solid generated by the rotation of R revolves around the right x = 0.
For (a) and (b), observe the following procedure:
- Draw a sketch (2D) of the R region and the axis of rotation.
- Calculate the points of intersection of the two curves.
- On this sketch, draw a standard rectangle.
- Clearly give the width height of this typical rectangle.
- Indicate which method you use (discs or tubes).
- Clearly give the definite integral (s) to be evaluated.
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