### Home > APCALC > Chapter 10 > Lesson 10.1.4 > Problem10-46

10-46.

Without your calculator, determine if each of the following integrals converges or diverges. Homework Help ✎

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

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

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

See the step in part (a).

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

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

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

See the step in part (c).