Volume of Revolved Area Bounded by ln(x) and the x-axis

[RadiationX]

Quesion on my final today!

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

Let $$y=\ln{x}\$$ bounded by $$x=e$$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? thanks in advance.

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

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

 

[learningphysics]

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

Let $$y=\ln{x}\$$ bounded by $$x=e$$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? thanks in advance.

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

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

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

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

 

[RadiationX]

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