Problem: Express the integrals in the opposite order. $$(a) \quad \int_{-\infty}^\infty \int_0^{\infty} f(x,y) \, dx \, dy$$ $$(b) \quad \int_{-\infty}^0 \int_0^{y^2} f(x,y) \, dx \, dy$$ $$(c) \quad \int_{-\infty}^\infty \int_0^x f(x,y) \, dy \, dx$$
Solution: $$(a) \ \ \int_{0}^\infty \int_{-\infty}^{\infty} f(x,y) \, dy \, dx\quad (b) \ \ \int_{0}^{\infty} \int_{-\infty}^{\sqrt{x}} f(x,y) \, dy \, dx\quad (c) \ \ \int_{0}^\infty \int_y^\infty f(x,y) \, dx \, dy$$
Are my solutions correct? Thanks.