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Math Help - Help with integral problem

  1. #1
    Junior Member TheMathTham's Avatar
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    Help with integral problem

    Hi everyone! First post here of many to come. I have an integral problem that I'm not sure on how to work out.

    (integral of)sin^(4)xcosxdx
    (If someone could tell me how to input the various math symbols, that would be much appreciated)

    The following are the answer choices:
    (A) .1sin^(5)xcos^(2)x + C
    (B) .2sin^(5)x + C
    (C) .2sin^(5)xcos^(2)x + C
    (D) 4sin^(3)xcos^(2)x-sin^(5)x + C
    (E) .2sin^(5)xcosx + sin^(5)x + C

    I'm pretty lost on what to do here. I can think of breaking up sin^(4)x into sin^(2)x * 1-cos^(2)x. Other than that, I'm not sure how to go about this problem. Thanks for any replies!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by TheMathTham View Post
    Hi everyone! First post here of many to come. I have an integral problem that I'm not sure on how to work out.

    (integral of)sin^(4)xcosxdx
    (If someone could tell me how to input the various math symbols, that would be much appreciated)

    The following are the answer choices:
    (A) .1sin^(5)xcos^(2)x + C
    (B) .2sin^(5)x + C
    (C) .2sin^(5)xcos^(2)x + C
    (D) 4sin^(3)xcos^(2)x-sin^(5)x + C
    (E) .2sin^(5)xcosx + sin^(5)x + C

    I'm pretty lost on what to do here. I can think of breaking up sin^(4)x into sin^(2)x * 1-cos^(2)x. Other than that, I'm not sure how to go about this problem. Thanks for any replies!
    let u=\sin{x}
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  3. #3
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    is it sin(4x) or sin^4(x)?.
    if it is sin^4(x) then u=sinx will do as von nemo said.
    and if it is sin4x then we can use (sin(5x)-sin(3x))/2 in place of sin(4x).cos(x).
    that should be integrable. hope this helps!!
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  4. #4
    Junior Member TheMathTham's Avatar
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    Quote Originally Posted by Pulock2009 View Post
    is it sin(4x) or sin^4(x)?.
    if it is sin^4(x) then u=sinx will do as von nemo said.
    and if it is sin4x then we can use (sin(5x)-sin(3x))/2 in place of sin(4x).cos(x).
    that should be integrable. hope this helps!!
    Now that I've learned the proper way to use the math symbols:
    \int {sin^4}xcosxdx

    von nemo was right, u-substitution did work, and I got B as the answer. Thanks!
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  5. #5
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    This website makes it easier to create the code for math problems.
    Online LaTeX Equation Editor
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