Dialation invariance of Lebesgue integral

Let $ f\in L^{1}(\mathbb{R}^d), a_1,\dots,a_d>0$ , and $ a=(a_1,\dots,a_d)$ . Define $ $ g(x)=f(a_1^{-1}x_1,\dots,a_d^{-1}x_d).$ $ Show that $ d\in L^{1}(\mathbb R^d)$ and that $ $ \int g=\left(\prod^{d}_{j=1}a_j\right)\int f.$ $ $…