## dfresenius 2 years ago Trig integrals. sqrt(1-cos2x)dx

1. dfresenius

|dw:1360952276270:dw|

2. dfresenius

should i do a u sub or change cos2x identity?

3. JamesJ

Well, cos(2x) = cos^2 x - sin^2 x = 1 - 2sin^2 x, hence $\sqrt{1 - \cos 2x} = \sqrt{1 - (1 - 2\sin^2 x)}$ which can be nicely simplified.

4. dfresenius

5. JamesJ

What does this expression simplify to? $\sqrt{1 - \cos 2x} = \sqrt{1 - (1 - 2\sin^2 x)}$

6. JamesJ

$\sqrt{1 - (1 - 2\sin^2 x)} = \sqrt{2\sin^2 x} = ...$

7. dfresenius

|dw:1360954273501:dw|

8. JamesJ

$\sqrt{1 - (1 - 2\sin^2 x)} = \sqrt{2\sin^2 x} = \sqrt{2} \sin x$ provided sin x > 0. Hence $\int \sqrt{1 - \cos 2x} \ dx \ = \ \int \sqrt{2} \sin x \ dx \ = \ ...$

9. dfresenius

sqrt(2)-cosx

10. dfresenius

$-\sqrt(2)cosx$

11. JamesJ

+ C, yes

12. dfresenius

from 0 to pi, the book asnwer says its 2sqrt2

13. dfresenius

i get 0

14. JamesJ

What is cos(pi) = ...? And cos(0) = ... ?

15. dfresenius

-1 and 1

16. dfresenius

sqrt(2) + sqrt(2) oh ya 2sqrt 2

17. dfresenius

sorry for wasting your time :(

18. JamesJ

np