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Integrating sin^2(x) and cos^2(x)

How do i integrate these? Ive tried but havent a clue.


sin^2(x)



cos^2(x)


(Its only an C3 AQA question btw)

thanks

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thereddevil
How do i integrate these? Ive tried but havent a clue.


sin^2(x)



cos^2(x)


(Its only an C3 AQA question btw)

ve just realised how stupid i was.
Reply 2
Avatar for Swayum
Swayum
18
Note that cos2x = cos^2x - sin^2x. Can you see how to use that in order to integrate them?
Reply 3
Avatar for wrockite
wrockite
Use double angle formulas

cos(2x) = 2[cos(x)]^2 - 1

cos(2x) = 1 - 2[sin(x)]^2

rearrange so you've got sin square x and cos square x in terms of cos(2x) and then they integrate easily
Reply 4
Avatar for studyboy
studyboy
13
thereddevil
How do i integrate these? Ive tried but havent a clue.


sin^2(x)



cos^2(x)


(Its only an C3 AQA question btw)

thanks


-1/2(cos^2x)

1/2(sin^2x)

Just treat it as normal but becareful with the 2(x) :smile:
Reply 5
Avatar for thereddevil
thereddevil
OP
1
studyboy
-1/2(cos^2x)

1/2(sin^2x)

Just treat it as normal but becareful with the 2(x) :smile:

I dont think its as simple as that.
Reply 6
Avatar for Swayum
Swayum
18
studyboy
-1/2(cos^2x)

1/2(sin^2x)

Just treat it as normal but becareful with the 2(x) :smile:


I think you're confusing sin2xsin^2x with sin(2x)sin(2x). The sin^2x notation means the former.
Reply 7
Avatar for thereddevil
thereddevil
OP
1
wrockite
Use double angle formulas

cos(2x) = 2[cos(x)]^2 - 1

cos(2x) = 1 - 2[sin(x)]^2

rearrange so you've got sin square x and cos square x in terms of cos(2x) and then they integrate easily

Core 3 qst so none of that....

the qst was find volume of rev thru 360

between y=0 to y=pi (not sure tho)

y = sin^(-1)x

so x=siny

V=pi (Integrate) (siny)^2 dy...............right?

so basically i think its integrate sin^2(x)
Reply 8
Avatar for 01s.clarke
01s.clarke
When you get to Core4 Edexcel (I don;t know if the books are the sameish for AQA) you find that the integral of Sin(^2)x dx = the integral of (1/2 - 1/2cos2x)dx as:

Cos2x = 1 - 2Sin(^2)x
So sin(^2)x = 1/2(1 - Cos2x)
So the integral of Sin(^2)dx = (1/2 - 1/2Cos2x)dx = 1/2x - 1/4Sin2x + C

Hope that helps with the Sin(^2)x one
Reply 9
Avatar for 01s.clarke
01s.clarke
The integral of Cos(^2)x = 1/2x + 1/4Sin2x + C but i cannot find the reason as yet, sorry. Hope this is of some help to you.
sin squared A = half(1-cos2A)

cos squared A = half(1 + cos2A)
Reply 11
Avatar for thereddevil
thereddevil
OP
1
I know all that sin(2x) stuff but i think that i must have used the wrong equation. (my previous post)
thereddevil
I know all that sin(2x) stuff but i think that i must have used the wrong equation. (my previous post)


you should be able to integrate from what i gave.

if it helps expand the right hand side (thus getting rid of the brackets) and it may be easier
Reply 13
Avatar for thereddevil
thereddevil
OP
1
hermaphrodite
you should be able to integrate from what i gave.

if it helps expand the right hand side (thus getting rid of the brackets) and it may be easier

but this is C3 not C4 or FP2:wink:
Reply 14
Avatar for Chewwy
Chewwy
17
give me strength.
Reply 15
Avatar for thereddevil
thereddevil
OP
1
Chewwy
give me strength.

sure why not.........in a maths forum?
Reply 16
Avatar for studyboy
studyboy
13
Swayum
I think you're confusing sin2xsin^2x with sin(2x)sin(2x). The sin^2x notation means the former.


Oh!! I see :p: :p: :p: My mistake! If this is the case then just use the double angle formula
Reply 17
Avatar for studyboy
studyboy
13
thereddevil
I dont think its as simple as that.


I'm sorry, I got confused with something else.:p:
Reply 18
Avatar for kexy
kexy
16
This is the most confusing thread I've seen on here... and it's not the maths that's confusing.
Reply 19
Avatar for thereddevil
thereddevil
OP
1
kexy
This is the most confusing thread I've seen on here... and it's not the maths that's confusing.

what?

lol

youre confusing!!:wink:

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