Question

Se f for continua e $\int\limits^9_0 {f(x)} \, dx =4$ , calcule $\int\limits^3_0 {xf(x^2)} \, dx$

Answer 1

$\displaystyle \int\limits_{0}^{3}xf(x^2)\,dx=\int\limits_{u(0)}^{u(3)}xf(u)\,dx\implies u=x^2\implies \frac{du}{2}=xdx\\\\ \frac{1}{2}\int\limits_{0}^{9}f(u)\,du=\frac{1}{2}\cdot4=\boxed{2}$