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sha0403

  • 2 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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  1. shubhamsrg
    • 2 years ago
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    let sinx = t

  2. Kainui
    • 2 years ago
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    Use "u"-substitution since you see a function and its derivative next to it.

  3. stgreen
    • 2 years ago
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  4. Kainui
    • 2 years ago
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    www.wolframalpha.com show me steps

  5. stgreen
    • 2 years ago
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    ^^shown

  6. Australopithecus
    • 2 years ago
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    you have to use identities to solve this \[\int\limits_{}^{}3 \sin^2 x \cos x\]

  7. Kainui
    • 2 years ago
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    ...

  8. Australopithecus
    • 2 years ago
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    \[3\int\limits_{}^{}\sin^2 x \cos xdx\] \[3\int\limits_{}^{}(1-\cos^{2}(x)) \cos xdx\]

  9. Kainui
    • 2 years ago
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    No, sin^2(x)=u 1/2 du=cosxdx 3/2udu becomes your new integral.

  10. Australopithecus
    • 2 years ago
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    f(x) = sin^2(x) f'(x) = cos(x)^2*sin(x)

  11. Chlorophyll
    • 2 years ago
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    Why not u = sinx --> du = cosxdx ??

  12. Chlorophyll
    • 2 years ago
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    = 3 ∫ u² du = ....

  13. Australopithecus
    • 2 years ago
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    \[3(\int\limits_{}^{}\cos(x)dx - \int\limits_{}^{}\cos^2(x)dx)\]

  14. Chlorophyll
    • 2 years ago
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    It's crystal clear about the relation between sinx and cosxdx :)

  15. Australopithecus
    • 2 years ago
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    remember for the future \[\cos^2(x) = \frac{1 + \cos(2x)}{2}\] so we have, \[3(\sin(x) + c - \int\limits_{}^{}\frac{1+\cos(2x)}{2}dx)\]

  16. stgreen
    • 2 years ago
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    ^done in 3rd reply

  17. Australopithecus
    • 2 years ago
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    You can solve it my way too which is good practice for when you get integrals with trig functions to high powers

  18. shubhamsrg
    • 2 years ago
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    @Australopithecus its cos^3 x there and not square

  19. Australopithecus
    • 2 years ago
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    oh sorry made a mistake lol

  20. sha0403
    • 2 years ago
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    where the best solution? i still confuse.. hu2

  21. Australopithecus
    • 2 years ago
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    it can still be solved with that method

  22. shubhamsrg
    • 2 years ago
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    and sinx= t ,u whatever, thats the easiest thing which you can do..as i pointed out in the very beginning ..

  23. shubhamsrg
    • 2 years ago
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    cos^3 x will still involve substitution ..

  24. Australopithecus
    • 2 years ago
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    \[3(\sin(x) + c - \int\limits_{}^{}\cos(x)\frac{1 + \cos(2x)}{2}dx\]

  25. Australopithecus
    • 2 years ago
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    I'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

  26. Australopithecus
    • 2 years ago
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    I think I made a mistake again though meh

  27. Kainui
    • 2 years ago
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    @Australopithecus It's like suggesting someone make a tunnel through a mountain when you can just use a teleporter.

  28. Australopithecus
    • 2 years ago
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    It is still applicable and stop hassling me I'm rusty ha

  29. sha0403
    • 2 years ago
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    so, the best solution? anyone?

  30. stgreen
    • 2 years ago
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    3rd

  31. Mathmuse
    • 2 years ago
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    @sha0403, to clarify, you should use any method provided except @Australopithecus'

  32. sha0403
    • 2 years ago
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    ok thanks u all for helping me..i appreciate it.. =)

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