- #1
roam
- 1,271
- 12
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) x2-4
2) 4-x2
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!
[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) x2-4
2) 4-x2
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!