Definite Integrals

#044 / Math Easy

Calculate the definite integral shown.

Expand Hint
$$$\int x^n \:dx=\frac{x^{n+1}}{n+1}$$$
Hint 2
After solving for the indefinite integral, plug in 10 as the upper integral boundary and 5 as the lower integral limit.
This is a two step calculus problem. First, let’s applying the power rule to solve the integral:
$$$\int \frac{1}{x^2}dx=\frac{x^{n+1}}{n+1}\:with\:n=-2$$$
$$$\int (x^{-2})dx=-\frac{1}{x}+C$$$
Next, solve using the upper integral boundary of 10, and lower integral limit of 5:
$$$(\frac{-1}{x})-(\frac{-1}{x})\rightarrow -\frac{1}{10}+\frac{1}{5}=-0.1+0.2=0.1$$$
0.1


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