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sha0403
 3 years ago
help me to integrate this :
integration of (3 sin^2 x cos x) dx
i confuse how to integrate this..
sha0403
 3 years ago
help me to integrate this : integration of (3 sin^2 x cos x) dx i confuse how to integrate this..

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Kainui
 3 years ago
Best ResponseYou've already chosen the best response.2Use "u"substitution since you see a function and its derivative next to it.

Kainui
 3 years ago
Best ResponseYou've already chosen the best response.2www.wolframalpha.com show me steps

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1you have to use identities to solve this \[\int\limits_{}^{}3 \sin^2 x \cos x\]

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1\[3\int\limits_{}^{}\sin^2 x \cos xdx\] \[3\int\limits_{}^{}(1\cos^{2}(x)) \cos xdx\]

Kainui
 3 years ago
Best ResponseYou've already chosen the best response.2No, sin^2(x)=u 1/2 du=cosxdx 3/2udu becomes your new integral.

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1f(x) = sin^2(x) f'(x) = cos(x)^2*sin(x)

Chlorophyll
 3 years ago
Best ResponseYou've already chosen the best response.0Why not u = sinx > du = cosxdx ??

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1\[3(\int\limits_{}^{}\cos(x)dx  \int\limits_{}^{}\cos^2(x)dx)\]

Chlorophyll
 3 years ago
Best ResponseYou've already chosen the best response.0It's crystal clear about the relation between sinx and cosxdx :)

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1remember for the future \[\cos^2(x) = \frac{1 + \cos(2x)}{2}\] so we have, \[3(\sin(x) + c  \int\limits_{}^{}\frac{1+\cos(2x)}{2}dx)\]

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1You can solve it my way too which is good practice for when you get integrals with trig functions to high powers

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.1@Australopithecus its cos^3 x there and not square

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1oh sorry made a mistake lol

sha0403
 3 years ago
Best ResponseYou've already chosen the best response.0where the best solution? i still confuse.. hu2

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1it can still be solved with that method

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.1and sinx= t ,u whatever, thats the easiest thing which you can do..as i pointed out in the very beginning ..

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.1cos^3 x will still involve substitution ..

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1\[3(\sin(x) + c  \int\limits_{}^{}\cos(x)\frac{1 + \cos(2x)}{2}dx\]

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1I'm not arguing that substitution will be involved in my solution but it still works for solving this integral it is just the long way

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1I think I made a mistake again though meh

Kainui
 3 years ago
Best ResponseYou've already chosen the best response.2@Australopithecus It's like suggesting someone make a tunnel through a mountain when you can just use a teleporter.

Australopithecus
 3 years ago
Best ResponseYou've already chosen the best response.1It is still applicable and stop hassling me I'm rusty ha

sha0403
 3 years ago
Best ResponseYou've already chosen the best response.0so, the best solution? anyone?

Mathmuse
 3 years ago
Best ResponseYou've already chosen the best response.0@sha0403, to clarify, you should use any method provided except @Australopithecus'

sha0403
 3 years ago
Best ResponseYou've already chosen the best response.0ok thanks u all for helping me..i appreciate it.. =)
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