Answer
$\int_{0}^{3}x~f(x^2)~dx = 2$
Work Step by Step
Let $u = g(x) = x^2$
Then $g'(x) = 2x$
According to the substitution rule:
$\int_{a}^{b}f(g(x))~g'(x)~dx = \int_{g(a)}^{g(b)}f(u)~du$
$\int_{0}^{3}f(x^2)~(2x)~dx = \int_{0}^{9}f(u)~du$
$2\cdot \int_{0}^{3}x~f(x^2)~dx = \int_{0}^{9}f(x)~dx$
$\int_{0}^{3}x~f(x^2)~dx = \frac{\int_{0}^{9}f(x)~dx}{2}$
$\int_{0}^{3}x~f(x^2)~dx = \frac{4}{2}$
$\int_{0}^{3}x~f(x^2)~dx = 2$
