Answer
(a) $\frac{5}{3}$
(b) $\frac{5}{3}$
(C) $\frac{-1}{2}$
Work Step by Step
(a) We find:
$\frac{1}{3} \int_{u(0)}^{u(1)} f(u) d u=\frac{1}{3} \int_{1}^{4} f(u) d u=\frac{5}{3}$
$d u=3 d x$ and $1+3 x=u$
(b) $\frac{1}{3} \int_{u(0)}^{u(3)} f(u) d u=\frac{1}{3} \int_{0}^{9} f(u) d u=\frac{5}{3}$
$3 d x=d u$ and $3 x=u$
(c) $\frac{1}{2} \int_{4}^{0} f(u) d u=\frac{1}{2} \int_{u(-2)}^{u(0)} f(u) d u=-\frac{1}{2}$
$2 x d x=d u$ and $x^{2}=u$
