Find the derivative of an integral

[IntegrateMe]

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

 

[Char. Limit]

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

 

[IntegrateMe]

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

 

[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.

 

[Dickfore]

The result is zero.

 

[elect_eng]

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

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?

 

[IntegrateMe]

Yes, sorry, it's d/dx

Wouldn't the result be just "sinx" ?

 

[Dickfore]

Yes, sorry, it's d/dx

Wouldn't the result be just "sinx" ?

yes.

 

[IntegrateMe]

Thank you! :)