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

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

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Reply 1

alexmunich0n

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

Swayum

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

Reply 3

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

studyboy

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

thereddevil

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

Swayum

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 $sin^2x$ with $sin(2x)$ . The sin^2x notation means the former.

Reply 7

thereddevil

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

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