[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

[alexmunich0n]

[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.

[Swayum]

Note that cos2x = cos^2x - sin^2x. Can you see how to use that in order to integrate them?

[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

[studyboy]

(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)

[thereddevil]

(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.

[Swayum]

(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.

[thereddevil]

(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)

[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

[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.

[hermaphrodite]

sin squared A = half(1-cos2A)

cos squared A = half(1 + cos2A)

[thereddevil]

I know all that sin(2x) stuff but i think that i must have used the wrong equation. (my previous post)

[hermaphrodite]

(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

[thereddevil]

(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

[Chewwy]

give me strength.

[thereddevil]

(Original post by Chewwy)
give me strength.

sure why not.........in a maths forum?

[studyboy]

(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

[studyboy]

(Original post by thereddevil)
I dont think its as simple as that.

I'm sorry, I got confused with something else.

[kexy]

This is the most confusing thread I've seen on here... and it's not the maths that's confusing.

[thereddevil]

(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!!