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Integral of (sin2x)^2

Barny

What is it? Im trying to do a volume generated around an axis question and Im not sure if Ive got the integral right..

Reply 1

Bezza

cos4x = 1 - 2*[sin(2x)]^2
[sin(2x)]^2 = [1-cos(4x)]/2
integral = x/2 - [sin(4x)]/8

Reply 2

Silly Sally

Bezza

cos4x = 1 - 2*[sin(2x)]^2
[sin(2x)]^2 = [1-cos(4x)]/2
integral = x/2 - [sin(4x)]/8

That was quick!!! :eek:

Reply 3

Bezza

Silly Sally

That was quick!!! :eek:

I can't help it :biggrin:

Reply 4

Barny

Bezza

cos4x = 1 - 2*[sin(2x)]^2
[sin(2x)]^2 = [1-cos(4x)]/2
integral = x/2 - [sin(4x)]/8

This is wrong

Reply 5

Silly Sally

imasillynarb

This is wrong

No it isn't, i just tried it and got exactly the same ans. I mean we could both be wrong but the chances prett slim me thinks!!! :smile:

Reply 6

Bezza

imasillynarb

This is wrong

Care to elaborate? (Try differentiating it, www.calc101.com if you want)

Reply 7

Barny

Silly Sally

No it isn't, i just tried it and got exactly the same ans. I mean we could both be wrong but the chances prett slim me thinks!!! :smile:

It doesnt give me the right answer for the volume generated, so it must be :frown:

Reply 8

Silly Sally

imasillynarb

It doesnt give me the right answer for the volume generated, so it must be :frown:

Well - just to make sure, does (sin2x)^2= 1/2(1 - cos4x)

Reply 9

Barny

Ooops, wait a minute, it does work, I didnt read the x/2 at first!! silly me :frown:

Reply 10

Silly Sally

You haven't forgotten to square the whole thing have you? The curve may be (sin2x)^2?

Reply 11

Bezza

imasillynarb

It doesnt give me the right answer for the volume generated, so it must be :frown:

What's the full question?

Sally - yes it does, my earlier link is a good place for checking integration/differentiation and it gives the same answer as us

Reply 12

Silly Sally

imasillynarb

Ooops, wait a minute, it does work, I didnt read the x/2 at first!! silly me :frown:

Reply 13

Silly Sally

Bezza

What's the full question?

Sally - yes it does, my earlier link is a good place for checking integration/differentiation and it gives the same answer as us

All sorted now!!! :biggrin:

Reply 14

Silly Sally

While on the subject of integration - can someone tell me whether it is possible to integrate:

e^(x^2)

I know we can differentiate it, but when integrating it, would the ans be:

1/x(e^(x^2))

Thanks :smile:

Reply 15

Bezza

Silly Sally

I'm pretty sure you can't integrate it, no.

Try differentiating what you have using the quotient rule - u = e^x^2, v = x
dy/dx = (vu' - uv')/v^2 = (x*2x*e^x^2 - e^x^2)/x^2 = e^x^2(2x^2 - 1)/x^2

Reply 16

Silly Sally

Bezza

I'm pretty sure you can't integrate it, no.

Try differentiating what you have using the quotient rule - u = e^x^2, v = x
dy/dx = (vu' - uv')/v^2 = (x*2x*e^x^2 - e^x^2)/x^2 = e^x^2(2x^2 - 1)/x^2

Well as long as i know i don't have to integrate it - then i am happy

I ALWAYS do this, i always wonder what would happen if a particular question is on the exam, then when i can't do it i begin to worry!!!

One of the reasons i am "silly" sally!!! :biggrin:

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