Chapter 15.1, Problem 52E

(a) In what way are the theorems of Fubini and Clairaut similar?

(b) If $f\left(x,y\right)$ is continuous on $\left[a,b\right]\times \left[c,d\right]$ and

$g\left(x,y\right)={\displaystyle {\int }_a^x{\displaystyle {\int }_c^{y}f\left(s,t\right)dtds}}$

for $a<x<b,c<y<d,$ show that $g_{xy}=g_{yx}=f\left(x,y\right)$.