Quesion on my final today!!!!

**RadiationX** · May6-05, 12:27 PM

I had the following question on my final exam today and i was wondering if i did it correctly:

Let $LaTeX Code: y=\\ln{x}\\$ bounded by

and the x-axis. Create a solid of revonution by revolving the are of R about the the line x=-1.

(a) use the cylindrical shell method.

(b) use the washer method

to find the volume of R.

We didn't have to evaluate the integrals. we just had to set them up
are my ansewers below correct? thx in advance.

$LaTeX Code: \\pi\\int_{0}^{1}{(e^y + 1)^2-1^2}dy$

$LaTeX Code: \\2\\pi\\int_{1}^e\\ln{x}(x +1)dx$

**learningphysics** · May6-05, 01:19 PM

Originally Posted by RadiationX

I had the following question on my final exam today and i was wondering if i did it correctly:

Let $LaTeX Code: y=\\ln{x}\\$ bounded by and the x-axis. Create a solid of revonution by revolving the are of R about the the line x=-1.

(a) use the cylindrical shell method.

(b) use the washer method

to find the volume of R.

We didn't have to evaluate the integrals. we just had to set them up
are my ansewers below correct? thx in advance.

$LaTeX Code: \\pi\\int_{0}^{1}{(e^y + 1)^2-1^2}dy$

$LaTeX Code: \\2\\pi\\int_{1}^e\\ln{x}(x +1)dx$

I finally got these:
cylindrical shell: $LaTeX Code: 2\\pi\\int_{1}^e\\ln{x}(x +1)dx$

washer: $LaTeX Code: \\pi\\int_{0}^{1}{(e + 1)^2-(e^y + 1)^2}dy$

**RadiationX** · May6-05, 02:51 PM

i got at least one correct. in my post i left off the 2pi for the last integral.thx