Chapter 5, Problem 27RE

Suppose that

${\displaystyle {\int }_0^{1}f\left(x\right)dx}=\frac{1}{2},{\displaystyle {\int }_1^{2}f\left(x\right)dx}=\frac{1}{4},$

${\displaystyle {\int }_0^{3}f\left(x\right)dx}=-1,{\displaystyle {\int }_0^{1}g\left(x\right)dx}=2$

In each part, use this information to evaluate the given integral, if possible. If there is not enough information to evaluate the integral, then say so.

(a) ${\displaystyle {\int }_0^{2}f\left(x\right)dx}$

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

(c) ${\displaystyle {\int }_2^{3}5f\left(x\right)dx}$

(d) ${\displaystyle {\int }_1^{0}g\left(x\right)dx}$

(e) ${\displaystyle {\int }_0^{1}g\left(2x\right)dx}$

(f) ${\displaystyle {\int }_0^1{\left[g\left(x\right)\right]}^2}dx$