InsideDarkWeb.com

Is taking the derivative inside this integral acceptable?

I have run into an integral where I take the partial derivative of x when the upper limit of the integral is x. This is how I solve it but I am not sure if this is correct. Can someone please check? Thank you!
$$ frac{partial}{partial x}int_0^xf(t)dt=int_0^xfrac{partial f(t)}{partial x}dt=0 $$

Mathematics Asked on November 18, 2021

1 Answers

One Answer

No.

Assuming that $x$ does not appear free in $f(t)$, then by the fundamental theorem of calculus:

$$dfrac{partial ~~}{partial x}int_0^x f(t)mathrm d t=f(x)$$

Answered by Graham Kemp on November 18, 2021

Add your own answers!

Related Questions

Using L’Hopital’s rule to find the limit of this function

1  Asked on January 18, 2021 by gregorystory16

 

The Cauchy-Crofton formula on a plane

1  Asked on January 18, 2021 by jalede-jale-uff-ne-jale

   

Galois group Abstract algebra

1  Asked on January 18, 2021 by user462999

   

Ask a Question

Get help from others!

© 2021 InsideDarkWeb.com. All rights reserved.