## Calculus: Early Transcendentals 8th Edition

Consider $f(x)=\frac{1}{x}$ and $g(x)=-\frac{1}{x}$, then $\int _{a}^{\infty}f(x)dx$ is divergent and $\int_{a}^{\infty}g(x)$ is divergent, but $\int _{a}^{\infty} (f(x)+g(x)) dx =\int _{a}^{\infty}0 dx=0$ is convergent. Hence, the given statement is false.