### Home > CALC > Chapter 10 > Lesson 10.1.4 > Problem10-32

10-32.

Without your calculator, determine if the following integrals are finite or not.

1. $\int _ { 1 } ^ { \infty } \frac { 1 } { x ^ { 0.9 } } d x$

$\lim\limits_{a\to\infty}\int_1^a\frac{1}{x^{0.9}}dx=\lim\limits_{a\to\infty}\int_{1}^{a}x^{-0.9}dx$

1. $\int _ { 1 } ^ { \infty } \frac { 1 } { x ^ { 1.1 } } d x$

See the step in part (a).

1. $\int _ { 0 } ^ { 1 } \frac { 1 } { x ^ { 0.9 } } d x$

$\lim\limits_{c\to 0}\int_c^1\frac{1}{x^{0.9}}dx=\lim\limits_{c\to 0}\int_{c}^{1}x^{-0.9}dx$

1. $\int _ { 0 } ^ { 1 } \frac { 1 } { x ^ { 1.1 } } d x$

See the step in part (c).