Integration Problem Solution Check: Is it Correct?

  • Thread starter mdnazmulh
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In summary, The conversation is about a student seeking confirmation on their integration solution. The problem given was \int(1- \frac{x}{a} )^{\frac{1}{n}} x dx and the student's attempt at a solution involved integration by parts, which the expert deemed unnecessary. They suggested a simpler method of multiplying and provided the simplified solution as \int (az^{1/n}- z^{(n+1)/n})dz.
  • #1
mdnazmulh
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Homework Statement



I solved the integration problem but i am not sure whether my solution is correct or wrong. I attached the picture of the solution.. Kindly tell me whether it is correct or wrong.

Homework Equations



This was the problem :
[tex]\int(1- \frac{x}{a} )^{\frac{1}{n}} x dx[/tex]

The Attempt at a Solution


 

Attachments

  • sltion.jpg
    sltion.jpg
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  • #2
I didn't check the whole thing since your solution is far more complicated than necessary. After you have, correctly, [itex]\int z^{1/n}(a- z)dz[/itex], do NOT use "integration by parts", just multiply:
[tex]\int (az^{1/n}- z^{1+1/n})dz= \int (az^{1/n}- z^{(n+1)/n})dz[/tex]
 

What is an integration problem?

An integration problem is a mathematical problem that involves finding the area under a curve. It involves the process of summing up infinitely many infinitely small rectangles under the curve to find the total area.

Why is it important to check if an integration problem solution is correct?

Checking the correctness of an integration problem solution is important because it ensures that the calculated answer is accurate and free from errors. It also helps to identify any mistakes made in the calculation process.

What are some common mistakes made when solving integration problems?

Some common mistakes made when solving integration problems include incorrect substitution, incorrect limits of integration, and algebraic errors. It is important to carefully check each step of the solution to avoid these errors.

How can I check if my integration problem solution is correct?

To check if your integration problem solution is correct, you can use a graphing calculator or online integration calculator to calculate the same integral. If the answers match, then your solution is likely correct. Additionally, you can also check your solution by differentiating it to see if it gives you the original integrand.

What should I do if my integration problem solution is incorrect?

If you find that your integration problem solution is incorrect, you should retrace your steps and check for any mistakes. It is also helpful to double-check your work using a different method or tool. If you are still unable to find the mistake, it is best to seek help from a teacher or tutor.

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