How to solve this integration problem problem did but got wrong answer

• mikhailpavel
In summary, the problem is asking to find the volume generated by rotating a region bound by the curves x=1+(y-2)^2 and x=2 about the x axis. The solution involves using the cylinder shells method, with an equation of integration of 2phiy(1+y^2-2y+4)dy and limits of 1 to 3. However, the length of the shell should be 2-(1+(y-2)^2), and upon correcting this, the final answer is found to be 142.42.
mikhailpavel

Homework Statement

Find the volume generated by rotating the region bound by the given curves about the x axis

x=1+(y-2)^2, x=2

The Attempt at a Solution

i solved the problem using cylinder shells method. the solution equation i got was
integration of 2phiy(1+y^2-2y+4)dy. the upper limit of the equation i got was 3 and the lower limit was 1.
the answer i got was 142.42 but it came out to be wrong.
can anyone help me.

The length of your shell should be 2-(1+(y-2)^2), right? When I expand that, I don't get (1+y^2-2y+4). Can you check that part?

thank you i got it now...what i did in my solution was that i didnt subtracted x=2 from the equation x= 1+ (y-2)^2.
thanks for the help.

1. How do I approach an integration problem?

When approaching an integration problem, it's important to first identify the type of integral you are dealing with. This can help determine the appropriate integration technique to use. Then, carefully apply the chosen technique, making sure to check for any potential mistakes along the way.

2. What are some common mistakes made when solving integration problems?

One common mistake is forgetting to use the chain rule when dealing with composite functions. Another is incorrectly applying the power rule, often by forgetting to add the "+C" constant at the end. It's also important to check for any algebraic errors or incorrect substitutions.

3. How do I know if I have the correct answer to an integration problem?

The best way to check if you have the correct answer is to differentiate your solution and see if it matches the original function. If it does, then your integral is most likely correct. You can also use online tools or ask a peer or instructor to verify your answer.

4. What should I do if I get stuck on an integration problem?

If you get stuck on an integration problem, take a step back and try to approach it from a different angle. Look for patterns or substitutions that may make the problem easier. You can also seek help from a classmate, tutor, or online resources for guidance.

5. How can I improve my integration skills?

The best way to improve your integration skills is through practice. The more problems you solve, the more familiar you will become with different techniques and patterns. You can also review your mistakes and seek help from a tutor or instructor to better understand the concepts behind integration.

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