Question

please helpppppppp...
question in comment

Answer 1

wht do u neep help with

Answer 2

the exact value is

Answer 3

re-write the integral using the identity and replacing the cube term

Answer 4

unable to do..

Answer 5

if A = B - C

\[\int B = \int A+C\]

Answer 6

the intergal will replace the cube term

Answer 7

i need detailed explanation if you dont mind !!!!!!!!

Answer 8

im talking bout u need to take 1/2 and replace it with the cube term which is 3

Answer 9

you have to integrate first????

Answer 10

ik thts wht i was telling u

Answer 11

will you help in donig it ?

Answer 12

who me

Answer 13

@phi

Answer 14

@mbma526

Answer 15

do you know how to integrate cos 3x ?

Answer 16

no

Answer 17

do you know how to integrate cos x ?

Answer 18

no @phi

Answer 19

do you know the derivative of sin x ?

Answer 20

-cosx

Answer 21

just cos x
\[ \frac{d}{dx} \sin x = \cos x \]
we can "undo the derivative" by integrating
\[ \int d \sin x = \int \cos x \ dx \\
\sin x = \int \cos x \ dx
\]

I'm not sure that is clear, but people memorize this integral
\[ \int \cos x \ dx = \sin x + C\]

Answer 22

but for \[\cos ^{3} x\] ??

Answer 23

let's first do cos 3x

if we let u= 3x
and we "work backwards"
\[ \frac{d}{dx} \sin u = \cos u \frac{d}{dx} u = \cos 3x \cdot 3\\
\frac{d}{dx} \sin 3x = 3 \cos 3x
\]

Answer 24

that is the derivative of sin 3x using the chain rule
if we want to integrate cos 3x
we need a 3 out front: 3 cos 3x
and to compensate , we multiply by 1/3

\[ \frac{1}{3} \int 3 \cos 3x \ dx = \frac{1}{3} \sin 3x \]

Answer 25

yes, there is a power of 3. patience.

Answer 26

hopefully you can integrate cos x and cos 3x (see above)
we are given
\[ \cos 3x =4 \cos^3 x - 3 \cos x \]
can you solve for cos^3 x ?

Answer 27

no not been able since 1 hour -___-

Answer 28

if you had
3= 4x + y
can you solve for x ?

Answer 29

yess x=(3-y)/4

Answer 30

use that same idea to "solve" (which means isolate to one side) cos^3 x
start with
\[ \cos 3x =4 \cos^3 x - 3 \cos x \]

Answer 31

didnt read the question well.. thank you @phi

Answer 32

you should get
\[ \cos^3 x = \frac{1}{4}\cos 3x + \frac{3}{4} \cos x \]

Answer 33

yesss thank you

Answer 34

now the integral
\[ \int \cos^3 x \ dx \]
can be written as
\[ \frac{1}{4}\int \cos 3x \ dx +\frac{3}{4} \int \cos x \ dx\]

Answer 35

yess i can do it further.. thank you

Answer 36

yw