You are Here: Home

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

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Enter our travel-writing competition for the chance to win a Nikon 1 J3 camera 21-05-2013
IMPORTANT: You must wait until midnight (morning exams)/4.30AM (afternoon exams) to discuss Edexcel exams and until 1pm/6pm the following day for STEP and IB exams. Please read before posting, including for rules for practical and oral exams. 28-04-2013
1. 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
2. Re: Integrating sin^2(x) and cos^2(x)
[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.
Last edited by alexmunich0n; 29-02-2008 at 22:56.
3. Re: Integrating sin^2(x) and cos^2(x)
Note that cos2x = cos^2x - sin^2x. Can you see how to use that in order to integrate them?
4. Re: Integrating sin^2(x) and cos^2(x)
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. Re: Integrating sin^2(x) and cos^2(x)
(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. Re: Integrating sin^2(x) and cos^2(x)
(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. Re: Integrating sin^2(x) and cos^2(x)
(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.
Last edited by Swayum; 29-02-2008 at 19:28.
8. Re: Integrating sin^2(x) and cos^2(x)
(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. Re: Integrating sin^2(x) and cos^2(x)
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. Re: Integrating sin^2(x) and cos^2(x)
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. Re: Integrating sin^2(x) and cos^2(x)
sin squared A = half(1-cos2A)

cos squared A = half(1 + cos2A)
12. Re: Integrating sin^2(x) and cos^2(x)
I know all that sin(2x) stuff but i think that i must have used the wrong equation. (my previous post)
13. Re: Integrating sin^2(x) and cos^2(x)
(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. Re: Integrating sin^2(x) and cos^2(x)
(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. Re: Integrating sin^2(x) and cos^2(x)
give me strength.
16. Re: Integrating sin^2(x) and cos^2(x)
(Original post by Chewwy)
give me strength.
sure why not.........in a maths forum?
17. Re: Integrating sin^2(x) and cos^2(x)
(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. Re: Integrating sin^2(x) and cos^2(x)
(Original post by thereddevil)
I dont think its as simple as that.
I'm sorry, I got confused with something else.
19. Re: Integrating sin^2(x) and cos^2(x)
This is the most confusing thread I've seen on here... and it's not the maths that's confusing.
20. Re: Integrating sin^2(x) and cos^2(x)
(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!!