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

  • Thread starter RadiationX
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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.
  • #1
RadiationX
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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 [tex]y=\ln{x}\ [/tex] bounded by [tex]x=e[/tex]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.

[tex]\pi\int_{0}^{1}{(e^y + 1)^2-1^2}dy[/tex]

[tex]\2\pi\int_{1}^e\ln{x}(x +1)dx[/tex]
 
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  • #2
RadiationX said:
I had the following question on my final exam today and i was wondering if i did it correctly:

Let [tex]y=\ln{x}\ [/tex] bounded by [tex]x=e[/tex]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.

[tex]\pi\int_{0}^{1}{(e^y + 1)^2-1^2}dy[/tex]

[tex]\2\pi\int_{1}^e\ln{x}(x +1)dx[/tex]

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

washer: [tex]\pi\int_{0}^{1}{(e + 1)^2-(e^y + 1)^2}dy[/tex]
 
  • #3
i got at least one correct. in my post i left off the 2pi for the last integral.thx
 

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

What material will the final cover?

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

How long will the final be?

The length of the final will depend on the specific instructions given by your instructor. It is best to check with them for the exact length of the final.

What type of questions will be on the final?

The final will likely consist of a combination of multiple choice, short answer, and essay questions. Be sure to review all material thoroughly to prepare for all types of questions.

Can I use notes or a calculator on the final?

This will also depend on the instructions given by your instructor. In most cases, notes and calculators are not allowed during the final. Be sure to check with your instructor for their specific policies.

What is the best way to prepare for the final?

The best way to prepare for the final is to review all material covered in the course. This can include studying lecture notes, completing practice questions, and reviewing any additional materials provided by your instructor.

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