### Home > APCALC > Chapter 10 > Lesson 10.1.3 > Problem10-31

10-31.

Determine the convergence or divergence of each of the following integrals. Homework Help ✎

1. $\int _ { - \infty } ^ { - 1 } \frac { 1 } { \sqrt { 2 - x } } d x$

$=\lim_{a\to-\infty}\int_{a}^{-1}\frac{1}{\sqrt{2-x}}dx$

$=\left.\lim_{a\to-\infty}\big(2-\sqrt{2-x}\big)\right|_{a}^{-1}$

$\lim_{a\to -\infty}(2\sqrt{3}-2\sqrt{2-a})$

1. $\int _ { - \infty } ^ { \infty } y ^ { 3 } d y$

$\lim_{b\to -\infty}\int_b^0 y^3dy+\lim_{b\to \infty}\int_0^b y^3dy$

1. $\int _ { 0 } ^ { 3 } \frac { 1 } { \sqrt { x } } d x$

$\lim_{c\to 0}\int_c^3\frac{1}{\sqrt{x}}dx$

1. $\int _ { 0 } ^ { \pi } \operatorname { sec } ( x ) d x$

$\sec(x)$ is undefined at $π/2$, so this integral will need to be split in two and limits used.

$\int\sec(x)dx=\ln\left|{\sec(x)+\tan(x)}\right|+C$