# Proof using FTC

## Homework Statement

Complete the proof by using the Fundamental Theorem of Calculus TWICE to establish
$$\int_c^d(\int_a^b f _{x}(x,y)dx)dy=...=\int_a^b(\int_{c}^{d}f_{x}(x,y) dy)dx$$

## Homework Equations

I know that the FTC states that if g(x)=\int_a^x(f), then g'=f

## The Attempt at a Solution

I'm not sure how to use this fact to get the proof started. Any guidance would be appreciated.

Last edited:

Mark44
Mentor

## Homework Statement

Complete the proof by using the Fundamental Theorem of Calculus TWICE to establish

$$\int_c^d(\int_a^b f _{x}(x,y)dx)dy=...=\int_a^b(\int_{c}^{d}f_{x}(x,y)dy)dx$$

## Homework Equations

I know that the FTC states that if g(x)=\int_a^x(f), then g'=f

## The Attempt at a Solution

I'm not sure how to use this fact to get the proof started. Any guidance would be appreciated.