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# Integral of (sin2x)^2 watch

1. What is it? Im trying to do a volume generated around an axis question and Im not sure if Ive got the integral right..
2. cos4x = 1 - 2*[sin(2x)]^2
[sin(2x)]^2 = [1-cos(4x)]/2
integral = x/2 - [sin(4x)]/8
3. (Original post by Bezza)
cos4x = 1 - 2*[sin(2x)]^2
[sin(2x)]^2 = [1-cos(4x)]/2
integral = x/2 - [sin(4x)]/8
That was quick!!!
4. (Original post by Silly Sally)
That was quick!!!
I can't help it
5. (Original post by Bezza)
cos4x = 1 - 2*[sin(2x)]^2
[sin(2x)]^2 = [1-cos(4x)]/2
integral = x/2 - [sin(4x)]/8
This is wrong
6. (Original post by 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!!!
7. (Original post by imasillynarb)
This is wrong
Care to elaborate? (Try differentiating it, www.calc101.com if you want)
8. (Original post by 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!!!
It doesnt give me the right answer for the volume generated, so it must be
9. (Original post by imasillynarb)
It doesnt give me the right answer for the volume generated, so it must be
Well - just to make sure, does (sin2x)^2= 1/2(1 - cos4x)
10. Ooops, wait a minute, it does work, I didnt read the x/2 at first!! silly me
11. You haven't forgotten to square the whole thing have you? The curve may be (sin2x)^2?
12. (Original post by imasillynarb)
It doesnt give me the right answer for the volume generated, so it must be
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
13. (Original post by imasillynarb)
Ooops, wait a minute, it does work, I didnt read the x/2 at first!! silly me
14. (Original post by 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!!!
15. 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
16. (Original post by 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
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
17. (Original post by 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!!!

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