# Thread: Multivariable differential with integral questions

1. ## Multivariable differential with integral questions

I am stucked after the last line. It seems there is no way to make the equality hold.

Thank you very much.

2. You missed some terms : for example we have $\displaystyle\int_{a_2}^{x_2}\dfrac{\partial f(x_1,t,a_3,\ldots,a_n)}{\partial x_2}\mathrm{d}t= f(x_1,x_2,a_3,\ldots,a_n)-f(x_1,a_2,a_3,\ldots,a_n)$.

3. I did have one more question. I deduced that from the fundamental theorem.

d/dx int (a to x) f(t)dt = f(x)

with no - f(a) entering.

While it appears here ?

Thanks a lot.

4. Indeed it doesn't appear in the first term, but it appear in the others because it's not the same differentiation (here it is differentiation under the symbol $\int$).

5. Thanks a lot I got it now.