Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=x^2+3x–10
y=0
about the x-axis.
I solved this problem by first solving the first equation and got [-5,2]. And then I used these numbers and performed the shell method and got my answer.
The answer I got when I did the problem was 69pi.
But when I checked the answer in the book. It said it was wrong. Can someone show me the steps on how to solve this problem?
Make sure you can visualise the solid itself.
Then, look at the function you're going to use* in the integration and visualise a single Reimman strip. Imagine the solid formed from revolving the strip round each axis. One way you should see a disc or washer, the other way a cylinder. One of them should fit nicely in the target solid - that tells you which formula to choose.
* assuming you've decided between y(x) vs. x(y) - but you can take each in turn.