Question

Integration by substitution.
Problem below.

Answer 1

\[\Large \int\limits \cos^3 \theta d \theta, \sin \theta = x\]

Answer 2

Put

\[u = \cos \theta \]

\[\frac{ du }{ d \theta } = -\sin \theta \]

\[du = -\sin \theta d \theta \]

Answer 3

\[-\int\limits_{}^{} u^3 du\]

Answer 4

hope nw u can Solve

Answer 5

i don't really get it. @Yahoo!

Answer 6

Which Part Confuses U ?

Answer 7

why you took u as cos?

Answer 8

To make it easier...think of a Condition where u take u = sin

Answer 9

du / d theta = cos theta

du = cos theta d teta

from..where we cant Substistute For u

Answer 10

@Yahoo! what about \[\Large \sin^3 \theta \cos^2 \theta d \theta, \cos \theta = x\]

Answer 11

\[\cos^3(\theta) = \cos(\theta)(\sin^2(\theta)-1)\]
Now, you can use u-substitution.

Answer 12

Nope. Don't get it.

Answer 13

\[\int\limits \cos^3(\theta)d \theta = \int\limits \cos(\theta)\cos^2(\theta)d \theta= \int\limits \cos(\theta)(\sin^2(\theta)-1)d \theta\]

Answer 14

Ohh this.. What about next one?

Answer 15

\[u = \sin(\theta)\]
\[du = \cos(\theta)\]
To get: \[\int\limits u^2-1 du\]

Answer 16

You follow a similar process factor out a cos, use trig identity and substitution.

Answer 17

\[\cos^2(x)\cos(x)\sin^2(x) \]

Answer 18

@saifoo.khan ...u got it?...or Shuld i write my Approach?