UsukiDoll
Quick question what is the antiderivative of 3sinxcosx?
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UsukiDoll
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wouldn't my u be sinx and du cosx?
mathslover
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Anti derivative .. hmn wait
mathslover
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Can we say ; antiderivative as "integration" also?
mayankdevnani
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@mathslover yes we can
mathslover
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@.Sam. Please let me try?
UsukiDoll
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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
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is it : \(\frac{-3}{2}cos^2x\) ?
mathslover
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OH + C there also
.Sam.
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\[\int\limits_{}^{}3sinxcosx~dx \\ \\ Let~u=sinx \\ \\du=cosx~dx \\ \\ Then, \\ \\ \int\limits_{}^{}3u~du \\ \\ Integrate\]
mathslover
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@UsukiDoll you were at right process.
.Sam.
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@mathslover oh sry didn't see your comment there.
mathslover
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:) 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
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\[\int\limits_{0}^{\frac{\pi}{2}}\] 3cos(x)sin(x)dx=\[\frac{3}{2}\]
UsukiDoll
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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
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@UsukiDoll ok got it
mayankdevnani
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@mathslover am i right
UsukiDoll
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sin^2t maybe but sin2t? what the heck
mathslover
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==lol
.Sam.
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@mathslover yes you are
ByteMe
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why not just u=sinx so du=cosxdx ???
UsukiDoll
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ummm that's what I did bytemr
UsukiDoll
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oops yes a =0 b = pi/2
ByteMe
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lol.... you said my name...
UsukiDoll
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loloolol
UsukiDoll
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I could've sworn it was like this...
|dw:1349253100916:dw|
hartnn
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3sinx cos x = 3/2 sin 2x
does this ring the bell ?
UsukiDoll
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Why is it sinx 2x?!?!?!?!?!?!?!!?
UsukiDoll
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is there an identity that I missed @hartnn
hartnn
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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
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yeah but that 2sinxcosx not 3sinxcosx and why is the 2 below the 3 in this one?
hartnn
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@mathslover you were typing something ?
3sin x cos x = 3/2 (2sin x cos x) = 3/2 sin 2x
hartnn
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its antiderivative will be -3/4 cos 2x
UsukiDoll
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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
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so u did not understand this ? 3sin x cos x = 3/2 (2sin x cos x)
i just multiplied and divided by 2
UsukiDoll
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ohhhhh..... -___-|dw:1349253933438:dw|
UsukiDoll
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that's legal? multiplying 2 and dividing 2?
hartnn
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absolutely!
because 2 is constant.
UsukiDoll
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O______O!
UsukiDoll
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ummm what math class is this normally in? Is it in trig?
hartnn
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those double angle formulas? in trignometry..
UsukiDoll
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no about the 3/2 2sinxcosx
hartnn
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its general, no particular topic, u can do that anytime, anywhere...
UsukiDoll
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THE HECK?
UsukiDoll
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I got one more...so I'm opening a new question.
hartnn
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ok.