Chapter 5.9, Problem 53ES

(a) Find ${\displaystyle {\int }_0^{1}f\left(3x+1\right)dx}$ if ${\displaystyle {\int }_1^{4}f\left(x\right)dx}=5$ .

(b) Find ${\displaystyle {\int }_0^{3}f\left(3x\right)dx}$ if ${\displaystyle {\int }_0^{9}f\left(x\right)dx}=5$ .

(c) Find ${\displaystyle {\int }_{-2}^{0}xf\left(x^2\right)dx}$ if ${\displaystyle {\int }_0^{4}f\left(x\right)dx}=1$ .