Integral help

W

wassupman

New member
Joined
Jul 2, 2020
Messages
8
Hello,
My Cal 2 class has asked the question below. I don't even know where to start. Can anyone help me?

"A solid is generated by rotating about the x-axis the region under the curve y=f(x), where f(x)>0 and x>=0. The volume of such a solid from 0 to b is b^2 for any b>0. Find f."
 
wassupman said:
Hello,
My Cal 2 class has asked the question below. I don't even know where to start. Can anyone help me?

"A solid is generated by rotating about the x-axis the region under the curve y=f(x), where f(x)>0 and x>=0. The volume of such a solid from 0 to b is b^2 for any b>0. Find f."
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
I second tkhunny's suggetion- if you knew f(x) how would you find the volume from 0 to b (probably using "disks" or "shells" and I have always preferred disks)? Write that out with the "f" inside the integral and set it equal to \(\displaystyle b^2\). Since f is inside the integral, consider differentiating.
 
Assume [MATH]\int f(x)^2 dx = F(x)[/MATH] and continue from there.
 
You must log in or register to reply here.
Top