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# 2) The region R in the first quadrant of the xy-plane is bounded by the curves...

2) The region R in the first quadrant of the xy-plane is bounded by the curves y=−3x^2+21x+54, x=0 and y=0. A solid S is formed by rotating R about the y-axis:

the (exact) volume of S is =

3) The region R in the first quadrant of the xy-plane is bounded by the curves y=−2sin(x), x=π, x=2π and y=0. A solid S is formed by rotating R about the y-axis:

the volume of S is =

4) The region bounded by x=1+y^2, x=0, y=1, and y=2 is rotated about the x-axis. Find the volume of the solid of revolution.

find the exact value

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