How is my integration wrong? X(

• Lo.Lee.Ta.
In summary, the conversation discusses a problem with taking an integral and getting a different answer than the expected one. The initial set-up for the integral is correct and when checked with Wolfram Alpha, the answer is 448π/15. However, when trying to solve it manually, the answer is 29.8666... which is rounded off. After further discussion and clarification, it is determined that the system may want the exact answer, not a rounded off decimal. The issue is resolved and the conversation ends with gratitude for the help.
Lo.Lee.Ta.
My set-up for the integral is right:

2$\pi$∫0 to 4 of (x)(√(4x) - (2x - 4))dx

= 2$\pi$∫(2x3/2 - 2x2 + 4)dx

When I Wolfram Alpha the answer, it is 448$\pi$/15.
The computer HW system counts that answer as correct.

But when I try to take the integral, it's wrong! :(

I did this...:

2$\pi$(2x5/2/5/2 - 2(x3)/3 + 4x2/4] |0 to 4

= 29.86$\pi$

...This is not right. But what's the matter with my integration?

Thanks SO much for the help! :)

Lo.Lee.Ta. said:
My set-up for the integral is right:

2$\pi$∫0 to 4 of (x)(√(4x) - (2x - 4))dx

= 2$\pi$∫(2x3/2 - 2x2 + 4)dx

When I Wolfram Alpha the answer, it is 448$\pi$/15.
The computer HW system counts that answer as correct.

But when I try to take the integral, it's wrong! :(

I did this...:

2$\pi$(2x5/2/5/2 - 2(x3)/3 + 4x2/4] |0 to 4

= 29.86$\pi$

...This is not right. But what's the matter with my integration?

Thanks SO much for the help! :)

Where did 4x^2/4 come from?

Oh, sorry. I wrote down (4x^2)/2 on my paper but typed it wrong!

I meant (4x^2)/2

Lo.Lee.Ta. said:
My set-up for the integral is right:

2$\pi$∫0 to 4 of (x)(√(4x) - (2x - 4))dx

= 2$\pi$∫(2x3/2 - 2x2 + 4)dx

When I Wolfram Alpha the answer, it is 448$\pi$/15.
The computer HW system counts that answer as correct.

But when I try to take the integral, it's wrong! :(

I did this...:

2$\pi$(2x5/2/5/2 - 2(x3)/3 + 4x2/4] |0 to 4

= 29.86$\pi$

...This is not right. But what's the matter with my integration?

Thanks SO much for the help! :)

448/15 = 29.8666666...

I'm guessing the system wants the exact answer, not a rounded off decimal.

Lo.Lee.Ta. said:
Oh, sorry. I wrote down (4x^2)/2 on my paper but typed it wrong!

I meant (4x^2)/2

Ok. 448/15=29.8666... What do you think is wrong??

Curious3141 said:
448/15 = 29.8666666...

I'm guessing the system wants the exact answer, not a rounded off decimal.

That's a good guess.

Yeah, I guess it was the rounding thing! Man! :/

Thank you SO much for helping! Simple problem! UGH! =_=

1. How do I know if my integration is wrong?

There are several signs that your integration may be wrong, such as incorrect results, errors or warnings, or unexpected behavior. It is important to thoroughly test and validate your integration to ensure its accuracy.

2. What are common mistakes in integration?

Common mistakes in integration include incorrect use of equations or formulas, incorrect input values, and insufficient testing. It is important to carefully review your integration process and double check all calculations and inputs.

3. How can I fix my integration if it is wrong?

If you have identified that your integration is wrong, the first step is to carefully review your code and check for any mistakes. It may also be helpful to consult with other experts in the field or seek additional resources for guidance. Once any errors have been corrected, be sure to thoroughly test and validate the updated integration.

4. How can I prevent making mistakes in my integration?

To prevent making mistakes in your integration, it is important to have a thorough understanding of the equations and formulas involved. It is also helpful to use reliable and accurate data sources and to carefully review and test your code before implementing it.

5. What should I do if I am unsure about my integration?

If you are unsure about your integration, it is best to seek guidance from experts in the field or consult additional resources. It is also important to thoroughly test and validate your integration to ensure its accuracy before using it for any important calculations or analyses.

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