## swin2013 Group Title Integral question? one year ago one year ago

1. swin2013 Group Title

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

2. swin2013 Group Title

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 Group Title

@zepdrix

4. zepdrix Group Title

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

5. zepdrix Group Title

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 Group Title

lol yea, i stated the lower boundary first

7. swin2013 Group Title

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

8. zepdrix Group Title

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 Group Title

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

10. swin2013 Group Title

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

11. zepdrix Group Title

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

12. zepdrix Group Title

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 Group Title

i know, I changed the theta values to u values

14. swin2013 Group Title

lol yea typo

15. swin2013 Group Title

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

16. zepdrix Group Title

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 Group Title

18. swin2013 Group Title

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

19. zepdrix Group Title

dat swin :3

20. swin2013 Group Title

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