Derivative of an integral with both limits as functions of x?

  • #1
264
0

Homework Statement



Find the derivative of:

[tex] \int_{tan(x)}^{2x^{2}} \frac {1}{\sqrt{1+t^{3}}} dt [/tex]

Homework Equations



[tex] \frac{d}{dx} \int_{a}^{x} f(t) dt = f(x) [/tex]

The Attempt at a Solution



I don't have an attempt because I do not know how to handle the problem... the FTC statement in 'Relevant equations' is only for the integral from a constant to a function of x, right? Help!
 

Answers and Replies

  • #2
fzero
Science Advisor
Homework Helper
Gold Member
3,119
289
You can pick a constant and write that integral as the difference of two integrals, each of which only has a single limit that is a function of x.
 
  • #3
182
0
Recall that the integral of f from a to b equals F(b) - F(a), where F' = f. Suppose there exists a function G(x) with the property that G'(x) = 1/(1+x^3). Don't forget the chain rule.
 

Related Threads on Derivative of an integral with both limits as functions of x?

Replies
4
Views
843
  • Last Post
Replies
2
Views
2K
Replies
12
Views
2K
Replies
3
Views
7K
Replies
17
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
1
Views
3K
Top