# Find the derivative of an integral!

1. Apr 18, 2010

### IntegrateMe

$$\frac {d} {dt}\int_{1}^{x} sint dt$$

2. Apr 18, 2010

### Char. Limit

This one is easy if you remember the First Fundamental Theorem of Calculus.

3. Apr 18, 2010

### IntegrateMe

Thanks, i guess i was just looking for what particular method to use.

4. Apr 18, 2010

### Char. Limit

Well, there are two methods...

You could solve the integral, which isn't too hard (the answer is cos(1)-cos(x)), and then differentiate it wrt x to reveal the function. But it's easier to just remember the FTC.

5. Apr 18, 2010

### Dickfore

The result is zero.

6. Apr 18, 2010

### elect_eng

Are you sure that you notated this correctly? It looks unusual to me. The integration would be done with respect to a variable t (essentially a dummy variable), and the result will be a function of x (the upper limit). The derivative of this with respect to t would then be zero.

Did you intend the derivative to be with respect to x?

7. Apr 18, 2010

### IntegrateMe

Yes, sorry, it's d/dx

Wouldn't the result be just "sinx" ?

8. Apr 18, 2010

### Dickfore

yes.

9. Apr 18, 2010

### IntegrateMe

Thank you! :)