# Definite integral

Karol

## Homework Statement

There is a problem in physics. i need to calculate the definite integral:
$$y=\int^{10}_2 \frac{13.2}{x^{1.4}}$$

## Homework Equations

$$\int x^{-a}=\frac{1}{-a+1}x^{-a+1}$$

## The Attempt at a Solution

$$y=\int^{10}_2 \frac{13.2}{x^{1.4}}=13.2\int^{10}_2 x^{-1.4}=13.2 \frac{1}{-0.4}x^{-0.4}|^{10}_2=-0.63$$
According to a graph i made with a graph software it came out -11.9, see picture

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Neither of these answers can be correct, you have the integral of a positive quantity and the result must be positive. I suggest rechecking your arithmetics.

You really should also consider always writing out the dx in the integral for clarity. The expressions are mathematically incomplete without it.

Karol
$$y=\int^{10}_2 \frac{13.2}{x^{1.4}}dx=13.2\int^{10}_2 x^{-1.4}dx=$$
$$=13.2 \frac{1}{-0.4}x^{-0.4}|^{10}_2=-33\left(\frac{1}{10^{0.4}}-\frac{1}{2^{0.4}}\right)=11.9$$

Staff Emeritus
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That looks much better and is correct as far as I can tell.

Karol
Thanks

$$y=\int^{10}_2 \frac{13.2}{x^{1.4}}dx=13.2\int^{10}_2 x^{-1.4}dx=$$
$$=13.2 \frac{1}{-0.4}x^{-0.4}|^{10}_2=-33\left(\frac{1}{10^{0.4}}-\frac{1}{2^{0.4}}\right)=11.9$$