## swin2013 2 years ago Integral question?

1. swin2013

$\int\limits \sin \theta (\cos \theta +5)^7 d \theta$

2. swin2013

My work: u = $\cos \theta + 5$ $du / d \theta$ : $\sin \theta$ du = $\sin \theta d \theta$ $\theta = \pi$ $\theta = 0$ u = 4 u = 6 $\int\limits\limits (from 4 - 6) u^7 du$

3. swin2013

@zepdrix

4. zepdrix

Hmm I think you're going from 6 to 4 actually aren't you?

5. zepdrix

Oh it looks like you missed the negative when you took the derivative of your u. Maybe you just applied it to your integral, swapping the limits of integration? Or maybe you got lucky? XD lol

6. swin2013

lol yea, i stated the lower boundary first

7. swin2013

so is it [-cos (theta + 5) ^8/8 ] from 4-6?

8. zepdrix

No, if you're going to go through the trouble of changing the limits, then it means you're going to solve (all the way down to a numerical value) in u, no longer worrying about the function of theta you had before.

9. zepdrix

$\large \frac{1}{8}u^8|_{u=4}^6$

10. swin2013

lol yea, the answer is 207, 760 but i don't get that :(

11. zepdrix

See how you changed the limits to u=? Those are values you'll be plugging into u. Simple as that.

12. zepdrix

It should be 201,760. Typo maybe? :o I'll check it on Wolfram real quick to make sure I didn't make a mistake.

13. swin2013

i know, I changed the theta values to u values

14. swin2013

lol yea typo

15. swin2013

oh... i thought that you replace u with u= costheta +5..

16. zepdrix

If you had not changed the limits of integration then yes you would have had to do that before putting in the limits. But you changed your limits ~ No need to change back to costheta+5.

17. zepdrix

18. swin2013

holy cow... i looked back at my notes. that is correct lol!

19. zepdrix

dat swin :3

20. swin2013

lollll thanks!! and i also have another question. but i'll post it on a different one lol