Question

Dear, Math talent.
Please help me with intergals

Answer 1

\[\int\limits_{?}^{?}(xcos(x^3))^2dx\]

Answer 2

heres ? in the question!

Answer 3

multiply it out first, will turn your integral into one that can be solved with a substitution.

Answer 4

there is a part missing.
is it equal to something?

Answer 5

@Dodo1 ?

Answer 6

No not equal!

Answer 7

@electrokid

Answer 8

It seems that the question is incomplete!!!

Answer 9

let me write it again

Answer 10

ok

Answer 11

if you can post a picture of the problem that would be nice too

Answer 12

\[\int\limits_{}^{}(xcos(x^3))^2)dx \]

Answer 13

sorry I wont be able to post photos my phone is not working but this is the question which is written in the paper.

Answer 14

in the original problem you have "?"symbols at the integration limits

Answer 15

it also says compute te following intergrals

Answer 16

Sorry theres no ?!

Answer 17

∫(xcos(x^3))2)dx=∫1/3x^3(cos(x^3))^2)dx=∫1/3(cos(x^3))2)dx^3=∫1/3(cost)^2dt
=∫1/3(cos2t/2+1/2)dt
u should be able to do the rest

Answer 18

thats what confused the people here...

so\[
\int[x\cos(x^3)]^2dx=\int x^2\cos^2(x^3)dx
\]
solve by substitution
\[u=x^3\implies du=3x^3dx\\
{du\over3}=x^2dx\]
so, we get
\[\int\cos^2(u){du\over3}={1\over3}\int\cos^2(u)du\]
then we have the double angle rule:
\[\cos^2\theta={\cos2\theta-1\over2}\]

Answer 19

so, it reduces to
\[{1\over3}\int\left(\cos(2u)-1\over2\right)du\\
\quad={1\over6}\int[\cos(2u)-1]du\\
\quad={1\over6}\left[????\right]
\]

Answer 20

you can solve from here :)

Answer 21

once you get the integration, replace "u" back by the substituion in "x"

Answer 22

cos2*x^3??

Answer 23

du =1/3?/

Answer 24

dont put in "x" yet..
lets solve the integral in terms of "u"

Answer 25

u(cos2)-(1)?

Answer 26

\[
{1\over6}\int\cos(2u)du-{1\over6}\int du
\]

Answer 27

I separated them

Answer 28

what is the integral of cos(2u)?

Answer 29

i am not 100 % the defition of integral...

Answer 30

is it derivative?

Answer 31

it is opposite of derivatives

"derivative of what is cos(2u)?"

Answer 32

cosu^2?

Answer 33

check.
do not guess
take the derivative of what you just said and see if you get cos(2u)

Answer 34

i am not guessing. i actually thought it was the answer.

Answer 35

hmm
whose derivative is cos(u)??

Answer 36

2cosu?

Answer 37

\[{d\over du}\sin(u)=?\]

Answer 38

o... from the rule.
cosx=sinx
sinx=-cosx ?

Answer 39

:D

Answer 40

those are the rules for integration