(adsbygoogle = window.adsbygoogle || []).push({}); 1. Evaluate

[tex]\int_{-1}^{3} \left|x^2 -4\right| dx[/tex]

3. The attempt at a solution

This is the first time I'm trying this type of question & I think I need to use the following theorem for such questions;

f is integrable on a closed interval a to b.

[tex]\int_{a}^{b}f(x)dx = \int_{a}^{c}f(x)dx + \int_{c}^{b}f(x)dx[/tex]

(c; any point in between, no matter how the points are ordered)

Therefore in my problem [tex]\int_{-1}^{3} \left|x^2 -4\right| dx[/tex], I choose c = 2

Now since the integrand is absolute value we have two cases:

1) x^{2}-4

2) 4-x^{2}

I'm not which one of the following is correct;

[tex]\int_{-1}^{2} (4-x^2)dx + \int_{2}^{3}(x^2 -4)dx[/tex]

OR

[tex]\int_{-1}^{2} (x^2-4)dx + \int_{2}^{3}(4-x^2)dx[/tex]

Which one is correct and why?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Absolute Value Integration

**Physics Forums | Science Articles, Homework Help, Discussion**