Thread: Volume integral set-up

1) Consider the region R bounded by:

x=4-y^2 and x=sqrt(4-y^2)

Find the volume of the solid that results when R is rotated about the y-axis.

2) Consider the region X bounded by:

x=1, y=2-x, and y=2e^x

Find the volume of the solid that results when X is rotated about the line x=2.

I just need help setting up the integrals, I can easily compute them. Thanks a bunch!

1)the equations given result into a parabola with vertex at(4,0) and a circle with radius 4 and centre at (0,0). so the region bounded by them is a point(correct me if i am wrong).so the volume will be 0.

Originally Posted by Pulock2009

1)the equations given result into a parabola with vertex at(4,0) and a circle with radius 4 and centre at (0,0). so the region bounded by them is a point(correct me if i am wrong).so the volume will be 0.

Actually, the second gives a circle of radius 2 with center at (0,0) but your point is still valid. Neither of the problems gives bounded region in the xy-plane to be rotated.

Was there some additional condition, like or ?

Originally Posted by twittytwitter

1) Consider the region R bounded by:

x=4-y^2 and x=sqrt(4-y^2)

...

Have a look at the drawing. Which of the bounded regions is meant?

(The parabola is not tangent to the circle!)

There is no additional specification, but I believe it is referring to the area between the circle and the parabola in Quadrants I and IV (i.e. positive x) So the big area between the parabola and circle in the positive x side, as well as the small areas on the top and bottom in the picture.

And actually I think the picture is not completely correct. It as given as x=sqrt(4-y^2), not x^2+y^2=4, and so, it should only be half a circle (the right half), no?