# Even and odd integrals

Find the definite integral

$$\int_{-2}^{2} \Big(2f(x) + 3g(x)\Big)dx$$

where $f(x)$ is an even function such that

$$\int_{0}^{2} f(x)dx = 3$$

and $g(x)$ is such that

$$\int_{-2}^{4} g(x)dx = -3 \ \ \text{and}\ \ \int_{2}^{4} g(x)dx = -6$$

• Hint: Split the integral up (addivitivity). Then split each of those integrals up again (property of integrals involving limits of integration). – user137731 Dec 14 '14 at 14:28