anonymous
  • anonymous
Any one out there who can give me a hand doing integrals
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Empty
  • Empty
\(\int\)ure, I can help probably.
anonymous
  • anonymous
\[\int\limits_{?}^{?} \sin2x/1+\cos^2x\]
anonymous
  • anonymous
In class, my teacher said to make the denominator = to u or p

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anonymous
  • anonymous
so let p= 1+cos^2x
anonymous
  • anonymous
dp =?
anonymous
  • anonymous
Yeah, let the bottom be your u. You will need an identity on the numerator to get the proper cancellation, though.
anonymous
  • anonymous
Take the derivative of p to get dp. Use the identity for the numerator sin 2x = 2 cos x sin x
anonymous
  • anonymous
where did you find the identity?
anonymous
  • anonymous
that's a double angle identity
anonymous
  • anonymous
oh
anonymous
  • anonymous
http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Double-angle.2C_triple-angle.2C_and_half-angle_formulae
anonymous
  • anonymous
can you give a hint on how to get dp
anonymous
  • anonymous
It's going to be the derivative of 1 + cosĀ² x. Use the chain rule
anonymous
  • anonymous
is it -2cosxsinx?
anonymous
  • anonymous
yes it is
anonymous
  • anonymous
with dx at the end?
anonymous
  • anonymous
yes
anonymous
  • anonymous
cool, but why? this is the stuff the confuses me
anonymous
  • anonymous
ohhhhhhhhhhhh
anonymous
  • anonymous
because there isn't an easy rule to integrate the original problem, so we use the substitution to make it simpler
anonymous
  • anonymous
u r the man
anonymous
  • anonymous
lol
anonymous
  • anonymous
The pic of Ernie is right on point too

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