## anonymous one year ago Evaluate the integral using integration by parts w/ the indicated choices of u and dv how do i do this? equation inside! thanks!!

1. anonymous

|dw:1442193899384:dw|

2. thomas5267

So the equation is: $\int\theta\cos(\theta)\,d\theta\\ u=\theta\\ dv=\cos(\theta)\,d\theta\\ \int u\,dv=uv-\int v\,du$

3. anonymous

yes:) i'm a bit confused, so i find du and v, right? would du = ø and v = -cosødø ?

4. zepdrix

Hmm if $$\large\rm u=\theta$$ then $$\large\rm du\ne\theta$$ You're taking a derivative with respect to theta :o $$\large\rm u'=1$$ yes?

5. anonymous

yes :) ohh so du = 1 ?

6. zepdrix

$\large\rm \color{orangered}{u'}=1$$\large\rm \color{orangered}{\frac{du}{d\theta}}=1\qquad\to\qquad du=1\cdot d\theta$

7. anonymous

ohh okay :) so which means du = dø ? and so would v be sinø ? :/

8. zepdrix

To get from $$\large\rm dv$$ to $$\large\rm v$$ you have to integrate. So going backwards from cosine gives us sine, ya that sounds right! :)$\large\rm dv=\cos\theta~d\theta\qquad\to\qquad v=\sin\theta$

9. anonymous

ooh yay!! :) and so now i do this?|dw:1442194685139:dw|

10. zepdrix

I wish you wouldn't use the "empty set" for your theta XD lol but ya looks good so far!

11. anonymous

ohh haha oops :P it's just more convenient using that symbol instead of drawing it :P and so would it get sin2ø - (-cosø)(ø) ?

12. anonymous

getting sin2ø + cos2ø + c ?

13. zepdrix

Hmm

14. zepdrix

In general: $$\large\rm a\cos(x)\ne\cos(ax)$$ You can't just bring stuff inside of the trig function willy nilly like that.

15. anonymous

ohh okay :( how do i do this part then? |dw:1442195029862:dw|

16. zepdrix

We leave this alone $$\large\rm \theta\sin\theta$$ that will be part of our final answer

17. zepdrix

$\large\rm -\int\limits\sin\theta~d\theta$Hmm looks like we made some kind of boo boo here on this integral.

18. zepdrix

If you ignore the negative out front, what is the integral of sine?

19. anonymous

cos ?

20. zepdrix

Hmm, no we're going backwards. Going forwards, derivative of sine is cosine.

21. anonymous

ohh - cos ?

22. zepdrix

$\large\rm -\color{orangered}{\int\limits\limits\sin\theta~d\theta}=\quad -\color{orangered}{(-\cos \theta+c)}$Mmm ya that sounds better!

23. zepdrix

So you have:$\large\rm \int\limits \theta \cos \theta~d \theta=\theta \sin \theta-(-\cos \theta+c)$

24. anonymous

ohh okay and so i simply it to øsinø + cos ø - c ?

25. zepdrix

Or even: $$\large\rm \theta\sin\theta+\cos\theta+C$$ absorb the negative into the c, since it can represent any negative or positive value.

26. anonymous

ahh okay! thank you!!:)

27. zepdrix

yay team \c:/