Integration q involving squared sign (1 Viewer)

[VenomP]

int. from pi/4 to 0 of cos^2 3x

What do you do here? My solutions look totally odd.

Is it a product rule? Would it be easier to use a chain rule or something?

Thanks.

 

[shaon0]

int. from pi/4 to 0 of cos^2 3x

What do you do here? My solutions look totally odd.

Is it a product rule? Would it be easier to use a chain rule or something?

Thanks.

cos^2 3x = 0.5(cos6x +1)
S cos^2 3x
= 0.5 S cos6x dx + 0.5 S 1 dx
= 1/12 sin6x + x/2 +C
Sub in the limits now.

Sorry its not that thorough. I'm a little busy.

 

[L]

transformations

 

[VenomP]

cos^2 3x = 0.5(cos6x +1)
S cos^2 3x
= 0.5 S cos6x dx + 0.5 S 1 dx
= 1/12 sin6x + x/2 +C
Sub in the limits now.

Sorry its not that thorough. I'm a little busy.

Sorry, this'll seem idiotic, but how did you work out the bolded line?

 

[lyounamu]

Sorry, this'll seem idiotic, but how did you work out the bolded line?

COS6X = 2cos^3(x) - 1
2cos^3(x) = cos6x + 1
cos^3(x)= 1/2(cos6x + 1)

 

[L]

COS6X = 2cos^3(x) - 1
2cos^3(x) = cos6x + 1
cos^3(x)= 1/2(cos6x + 1)

hi

im a tool

oh wait, no lol

thats you.

 

[VenomP]

COS6X = 2cos^3(x) - 1
2cos^3(x) = cos6x + 1
cos^3(x)= 1/2(cos6x + 1)

What does 2cos^3(x) have to do with anything when the question involves cos^2 3x?

I'm not being mean here, even though it sounds it. I really do appreciate your help.

 

[xtcy]

hi

im a tool

oh wait, no lol

thats you.

hahahaha good one.

sup jamie, how was shopping?

 

[L]

hahahaha good one.

sup jamie, how was shopping?

lol, didnt go

woke up and couldn't summon the energy to leave the house

tomorrow.

 

[SeftonIsAHole]

What does 2cos^3(x) have to do with anything when the question involves cos^2 3x?

I'm not being mean here, even though it sounds it. I really do appreciate your help.

you're manipulating the question to make it simple to integrate by using trig rules..[double angle cosine]

 

[addikaye03]

Since cos2x=2cos^2x-1 OR 1-2sin^2x, therefore cos4x=2cos^2(2x)-1, then cos8x=2cos^2(4x)-1 therefore cos6x=2cos^2(3x)-1, by rearranging 2cos^2(3x)=cos6x+1 and cos^2(3x)=0.5(cos6x+1), then int. accordingly

Remember the process, dont remember the transformation, theres already enough shit to remember