some integration questions

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yu.doll@gmail.com - 04 Jul 2007 03:23 GMT

hi, i am going over multiple integrals for the test and i came across
a few examples which are unclear. it has to do with some really basic
rule that i am missing.
here's one:

/pi/2 /
cosx /
pi/2
| | e^sinx dr dx - as a result of first integration we
end up getting | e^sinx cosx dx =
/0 /
0 /
0
| pi/2
= e^sinx| ....my question is how did we end up getting
e^sinx after integrating e^sinx cosx?
|0

and a very simple integration that i am not following...why do we get -
cosx^2/2 when we integrate xsinx^2?

thats all, folks

thanks in advance

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yu.doll@gmail.com - 04 Jul 2007 03:27 GMT

completely screwed up the format..here's the condensed version.

= why do we get e^sinx when we integrate e^sinx cos x?
= why do we get -cosx^2/2 when we integrate xsinx^2?

thanks!

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ooo - 04 Jul 2007 03:45 GMT

>completely screwed up the format..here's the condensed version.
>
>= why do we get e^sinx when we integrate e^sinx cos x?

Make the substitution

u = sin(x) du = cos(x) dx, giving

Int e^u du

= e^u

= e^sin(x)

>= why do we get -cosx^2/2 when we integrate xsinx^2?

Make the substitution

u = x^2 du = 2x dx du/2 = x dx, giving

Int 1/2 sin(u) du

= -1/2 cos(u)

= -1/2 cos(x^2)

>thanks!

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Frederick Williams - 04 Jul 2007 14:56 GMT

> completely screwed up the format..here's the condensed version.
>
> = why do we get e^sinx when we integrate e^sinx cos x?

Why not ask yourself: what is the derivative of e^{sin x}?

> = why do we get -cosx^2/2 when we integrate xsinx^2?

Why not ask yourself: what is the derivative of -cos(x^2/2)?

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mathhelp123 - 28 Aug 2007 21:09 GMT

Use www.logicace.com, it can give you detailed steps.

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Math Forum / Mathematics / Undergraduate Math / August 2007

some integration questions