# Thread: Volumes of Integration (Tricky Problem involving both an x and y value)

1. ## Volumes of Integration (Tricky Problem involving both an x and y value)

I can't seem to get this. Can someone please show me how one would go about solving this?

Find the volume of the solid obtained by rotating the region bounded by the x- axis, the line y = 1, the curve y = ln(x), and the line x = 1/2 about the y-axis.

Thanks.

2. ## Re: Volumes of Integration (Tricky Problem involving both an x and y value)

washers
with dy and y=0 to y=1
outer radius is the logarithm, the inner is .5.
I haven't done one of these in over 10 years.
I think it's...

$\displaystyle \pi\int_0^1 \left[(e^y)^2-(.5)^2 \right]dy$

3. ## Re: Volumes of Integration (Tricky Problem involving both an x and y value)

Originally Posted by bhaktir
I can't seem to get this. Can someone please show me how one would go about solving this?

Find the volume of the solid obtained by rotating the region bounded by the x- axis, the line y = 1, the curve y = ln(x), and the line x = 1/2 about the y-axis.

Thanks.
Start by sketching the region that is to be rotated. You'll see that this will be easiest to solve by rotating a larger (easier) region and subtracting another easy region.