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

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1. 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
2. [QUOTE=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.
3. Note that cos2x = cos^2x - sin^2x. Can you see how to use that in order to integrate them?
4. 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
5. (Original post by 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)
6. (Original post by studyboy)
-1/2(cos^2x)

1/2(sin^2x)

Just treat it as normal but becareful with the 2(x)
I dont think its as simple as that.
7. (Original post by studyboy)
-1/2(cos^2x)

1/2(sin^2x)

Just treat it as normal but becareful with the 2(x)
I think you're confusing with . The sin^2x notation means the former.
8. (Original post by 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)
9. 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
10. 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.
11. sin squared A = half(1-cos2A)

cos squared A = half(1 + cos2A)
12. I know all that sin(2x) stuff but i think that i must have used the wrong equation. (my previous post)
13. (Original post by 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
14. (Original post by 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
15. give me strength.
16. (Original post by Chewwy)
give me strength.
sure why not.........in a maths forum?
17. (Original post by Swayum)
I think you're confusing with . The sin^2x notation means the former.
Oh!! I see My mistake! If this is the case then just use the double angle formula
18. (Original post by thereddevil)
I dont think its as simple as that.
I'm sorry, I got confused with something else.
19. This is the most confusing thread I've seen on here... and it's not the maths that's confusing.
20. (Original post by 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!!

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