Chapter 5.5, Problem 105E

To determine

To prove: The statement ${\displaystyle \underset{a}{\overset{b}{\int }}f\left(cx\right)dx}=\frac{1}{c}{\displaystyle \underset{ac}{\overset{bc}{\int }}f\left(u\right)du}$ by using the scaling $u=cx$, where $c$ is a real number and then draw the picture to illustrate this change of variable in the case $f\left(x\right)=\sin x,a=0,b=\pi \text{and }c=\frac{1}{2}$.