Question

Integral question?

Answer 1

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

Answer 2

My work:

u = \[\cos \theta + 5\]
\[du / d \theta\] : \[\sin \theta\]
du = \[\sin \theta d \theta \]

\[\theta = \pi \]
\[\theta = 0 \]
u = 4
u = 6

\[\int\limits\limits (from 4 - 6) u^7 du \]

Answer 3

@zepdrix

Answer 4

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

Answer 5

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

Answer 6

lol yea, i stated the lower boundary first

Answer 7

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

Answer 8

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.

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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.

Answer 13

i know, I changed the theta values to u values

Answer 14

lol yea typo

Answer 15

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

Answer 16

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.

Answer 17

Confused about that part? <:o

Answer 18

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

Answer 19

dat swin :3

Answer 20

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