Chapter 4.2, Problem 50E

Use geometry and the following graph of $f\left(x\right)=\frac{1}{2}x$ to evaluate each definite integral.

a. ${\displaystyle {\int }_0^{1}f\left(x\right)dx}$

b. ${\displaystyle {\int }_1^{3}f\left(x\right)dx}$

c. Find c such that ${\displaystyle {\int }_0^{c}f\left(x\right)dx}=4$

d. Find c such that ${\displaystyle {\int }_0^{c}f\left(x\right)dx}=3$.