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Integration of many variables

  • Thread starter soopo
  • Start date
  • #1
225
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Homework Statement


Let
F(x) = integral from x to 1 ( [tex]3t^3 - x^2 t ) dt[/tex]

1. Calculate F'(x)

The Attempt at a Solution



I know the answer is

x^3 + x.

However, I am not sure how it is obtained.

I know about implicit differentian, but I have never done implicit integration.

How can you solve the problem?
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
In this case, you can simply work out the integral.
Do the t-integration, it will give you
[tex]\frac34 t^4 - \frac12 x^2 t^2[/tex]
evaluated between the boundaries t = x and t = 1.
Then differentiate.
 
  • #3
225
0
In this case, you can simply work out the integral.
Do the t-integration, it will give you
[tex]\frac34 t^4 - \frac12 x^2 t^2[/tex]
evaluated between the boundaries t = x and t = 1.
Then differentiate.
Thank you for your answer!

The solution was much easier than I first thought.
 

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