anonymous
  • anonymous
evaluate indefinite integrals intergral tan^2x Sec^2x dx
Calculus1
chestercat
  • chestercat
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anonymous
  • anonymous
tanx=u
anonymous
  • anonymous
take the derivative
anonymous
  • anonymous
derivative of tanx?

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anonymous
  • anonymous
both sides
anonymous
  • anonymous
what is it
anonymous
  • anonymous
derivative of tna is sec^2x
anonymous
  • anonymous
sec^2xdx=du
anonymous
  • anonymous
subs. them in int.
anonymous
  • anonymous
if tanx=u then what is tan^2x
anonymous
  • anonymous
u sqre
anonymous
  • anonymous
good
anonymous
  • anonymous
then what is your new int. depends on only u
anonymous
  • anonymous
int. tan^2x Sec^2x dx sec^2xdx=du tan^2x=u^2
anonymous
  • anonymous
csc x^3/ 3 ?
anonymous
  • anonymous
|dw:1355646302656:dw|
anonymous
  • anonymous
what are they in u
anonymous
  • anonymous
u^2 . du
anonymous
  • anonymous
yesssssss..
anonymous
  • anonymous
solve that integral..
anonymous
  • anonymous
1/3 tan^3 x+c ?
anonymous
  • anonymous
you got it..
anonymous
  • anonymous
but i have one question though
anonymous
  • anonymous
shoot it..
anonymous
  • anonymous
|dw:1355639354738:dw|
anonymous
  • anonymous
|dw:1355646949637:dw|
anonymous
  • anonymous
did not get it,s orry
anonymous
  • anonymous
they are the same thing but just different letter..
anonymous
  • anonymous
|dw:1355647192985:dw|
anonymous
  • anonymous
oh okay.
anonymous
  • anonymous
dx or du they are just saying that you are taking int. depends on that variable
anonymous
  • anonymous
|dw:1355647315134:dw|
anonymous
  • anonymous
you can assume that x is just a constant in here..
anonymous
  • anonymous
okay,thanks. i have another problem, will you help me with that?
anonymous
  • anonymous
ok..
anonymous
  • anonymous
thanks
anonymous
  • anonymous
|dw:1355640103615:dw|
anonymous
  • anonymous
|dw:1355647649309:dw|
anonymous
  • anonymous
take derivative
anonymous
  • anonymous
how do you decide which one is "U"?
anonymous
  • anonymous
(:
anonymous
  • anonymous
because I can see that derivative sinx =cosxdx and it is above
anonymous
  • anonymous
|dw:1355647787810:dw|
anonymous
  • anonymous
derivative of sin theta = cos theta d theta
anonymous
  • anonymous
but it is sinsqrt theta
anonymous
  • anonymous
cos sqrt theta d theta
anonymous
  • anonymous
|dw:1355647993776:dw|
anonymous
  • anonymous
one more thing youre missing
anonymous
  • anonymous
what is it?
anonymous
  • anonymous
derivative of sqrt theta
anonymous
  • anonymous
|dw:1355640793032:dw|
anonymous
  • anonymous
|dw:1355648238516:dw|
anonymous
  • anonymous
|dw:1355648283456:dw|
anonymous
  • anonymous
how did you get that half?
anonymous
  • anonymous
|dw:1355648328997:dw|
anonymous
  • anonymous
|dw:1355648354029:dw|
anonymous
  • anonymous
|dw:1355648407558:dw|
anonymous
  • anonymous
what is your new integral..
anonymous
  • anonymous
|dw:1355648571843:dw|
anonymous
  • anonymous
1/2 integral 1/sin sqrt theta +c?
anonymous
  • anonymous
|dw:1355648717143:dw|
anonymous
  • anonymous
|dw:1355648783325:dw|
anonymous
  • anonymous
confused
anonymous
  • anonymous
what is int. 1/x dx=?
anonymous
  • anonymous
d
anonymous
  • anonymous
x
anonymous
  • anonymous
|dw:1355648969297:dw|
anonymous
  • anonymous
okay
anonymous
  • anonymous
in your case lnu+c put u back in
anonymous
  • anonymous
I gotta go, any question..
anonymous
  • anonymous
so,thats the ans ? after putting the u?
anonymous
  • anonymous
yes, ln(sin sqrt theta)+c is the answer..
anonymous
  • anonymous
okay,thanks a lot
anonymous
  • anonymous
np..

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