- #1

Lee33

- 160

- 0

## Homework Statement

Let ##[a,b]## and ##[c,d]## be closed intervals in ##\mathbb{R}## and let ##f## be a continuous real valued function on ##\{(x,y)\in E^2 : x\in[a,b], \ y\in[c,d]\}.## We have that ##\int^d_c\left(\int^b_af(x,y)dx\right)dy## and ##\int^b_a\left(\int^d_cf(x,y)dy\right)dx## exist.

## Homework Equations

None

## The Attempt at a Solution

I am wondering how this was solved?

Why is that from the fundamental theorem of calculus we get ##\frac{d}{dt}\int^t_a\left(\int^d_cf(x,y)dy\right)dx## ##=## ##\int^d_cf(t,y)dy## ?