## anonymous 3 years ago How do you evaluate the following integral analytically (no graphs, or calculators)?

1. anonymous

$\int\limits_{0}^{5}\left| (x^2-5x+4) \right| dx$

2. anonymous

Thanks! How did you get those 3 parts (this is kinda dumb, but sorry).

3. anonymous

when you put x=1 the absolute value is positive when you put x=2 and three absolute value is negative (thats why i put - sign in front of second integral ) for x=4 and 5 absolute value is again positive .

4. anonymous

Isn't it 0 @ 1?

5. anonymous

yes it is because at x=0 still abs (x^-5x+4) =(0-0+4)=4 positive .

6. anonymous

Should the second integral be from 1 to 4 instead of 1 to 3, and the third integral be from 4 to 5?

7. anonymous

at x=1 yes zero .

8. anonymous

so the second integral should be from 1 to 4, and the 3rd one 4 to 5?

9. anonymous

sorry i wrote it wrong . you are right first from 0..1 second from 1..4 and third from 4..5

10. anonymous

$\Large \int\limits_{0}^{1} (x^2-5x+4)dx-\int\limits_{1}^{4} (x^2-5x+4)dx+\int\limits_{4}^{5}(x^2-5x+4)dx$