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

In summary, the conversation was about a question on a final exam involving finding the volume of a solid of revolution using the cylindrical shell and washer methods. The integrals were set up but not evaluated. The correct answers were 2\pi\int_{1}^e\ln{x}(x +1)dx for the cylindrical shell method and \pi\int_{0}^{1}{(e + 1)^2-(e^y + 1)^2}dy for the washer method.
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.

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

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

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

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

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The final will cover all material that has been taught throughout the course. This includes lectures, readings, and any additional materials discussed in class.

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