UsukiDoll
  • UsukiDoll
Quick question what is the antiderivative of 3sinxcosx?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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UsukiDoll
  • UsukiDoll
wouldn't my u be sinx and du cosx?
mathslover
  • mathslover
Anti derivative .. hmn wait
mathslover
  • mathslover
Can we say ; antiderivative as "integration" also?

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mayankdevnani
  • mayankdevnani
@mathslover yes we can
mathslover
  • mathslover
@.Sam. Please let me try?
UsukiDoll
  • UsukiDoll
I just need to know what the antiderivate of 3sinxcosx is and yes I am integrating from crud hold up let me find it. Got hazelnut on my fingers
mathslover
  • mathslover
is it : \(\frac{-3}{2}cos^2x\) ?
mathslover
  • mathslover
OH + C there also
.Sam.
  • .Sam.
\[\int\limits_{}^{}3sinxcosx~dx \\ \\ Let~u=sinx \\ \\du=cosx~dx \\ \\ Then, \\ \\ \int\limits_{}^{}3u~du \\ \\ Integrate\]
mathslover
  • mathslover
@UsukiDoll you were at right process.
.Sam.
  • .Sam.
@mathslover oh sry didn't see your comment there.
mathslover
  • mathslover
:) No problem @.Sam. , it is so nice of you to even say "sry" no mistake of yours' . Though, can you tell whether I am correct or not (scroll up to see my answer)
mayankdevnani
  • mayankdevnani
\[\int\limits_{0}^{\frac{\pi}{2}}\] 3cos(x)sin(x)dx=\[\frac{3}{2}\]
UsukiDoll
  • UsukiDoll
I need the antiderivative of 3sinxcosx integrating from pi/2 to 0. umm that's what I did. like u sinx du cosx and then it's 3/2 u^2 but for some reason my manual has it at 3/2 sin2t. ummm WHAT!
mayankdevnani
  • mayankdevnani
@UsukiDoll ok got it
mayankdevnani
  • mayankdevnani
@mathslover am i right
UsukiDoll
  • UsukiDoll
sin^2t maybe but sin2t? what the heck
mathslover
  • mathslover
==lol
.Sam.
  • .Sam.
@mathslover yes you are
anonymous
  • anonymous
why not just u=sinx so du=cosxdx ???
UsukiDoll
  • UsukiDoll
ummm that's what I did bytemr
UsukiDoll
  • UsukiDoll
oops yes a =0 b = pi/2
anonymous
  • anonymous
lol.... you said my name...
UsukiDoll
  • UsukiDoll
loloolol
UsukiDoll
  • UsukiDoll
I could've sworn it was like this... |dw:1349253100916:dw|
hartnn
  • hartnn
3sinx cos x = 3/2 sin 2x does this ring the bell ?
UsukiDoll
  • UsukiDoll
Why is it sinx 2x?!?!?!?!?!?!?!!?
UsukiDoll
  • UsukiDoll
is there an identity that I missed @hartnn
hartnn
  • hartnn
double angle formula: sin 2x = 2 sin x cos x cos 2x = cos^2 x- sin^2 x = 2cos^2x -1 = 1-2sin^2 x
UsukiDoll
  • UsukiDoll
yeah but that 2sinxcosx not 3sinxcosx and why is the 2 below the 3 in this one?
hartnn
  • hartnn
@mathslover you were typing something ? 3sin x cos x = 3/2 (2sin x cos x) = 3/2 sin 2x
hartnn
  • hartnn
its antiderivative will be -3/4 cos 2x
UsukiDoll
  • UsukiDoll
again what I don't understand is why the 3/2? the problem is 3sinxcosx. There is no 2sinxcosx. so what Do i DO?
hartnn
  • hartnn
so u did not understand this ? 3sin x cos x = 3/2 (2sin x cos x) i just multiplied and divided by 2
UsukiDoll
  • UsukiDoll
ohhhhh..... -___-|dw:1349253933438:dw|
UsukiDoll
  • UsukiDoll
that's legal? multiplying 2 and dividing 2?
hartnn
  • hartnn
absolutely! because 2 is constant.
UsukiDoll
  • UsukiDoll
O______O!
UsukiDoll
  • UsukiDoll
ummm what math class is this normally in? Is it in trig?
hartnn
  • hartnn
those double angle formulas? in trignometry..
UsukiDoll
  • UsukiDoll
no about the 3/2 2sinxcosx
hartnn
  • hartnn
its general, no particular topic, u can do that anytime, anywhere...
UsukiDoll
  • UsukiDoll
THE HECK?
UsukiDoll
  • UsukiDoll
I got one more...so I'm opening a new question.
hartnn
  • hartnn
ok.

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