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Math Help - integration and another qn.

  1. #1
    Member helloying's Avatar
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    integration and another qn.

    Find \int\sin^2 (3x+2) dx


    and also another qn which i am not sure it belong to which catagory so i just post it here together with the previous qn.

    the cubic polynomial is such that the coefficient of x^3is -2 ans the roots of the eqn f(x)=0 are 0.5,2 and k

    Given that f(x) has a remainder -20 when divided by (x+2), find the value of k.

    thank you
    Last edited by helloying; June 26th 2009 at 08:13 PM.
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by helloying View Post
    the cubic polynomial is such that the coefficient of [tex]x^3[\math]is -2 ans the roots of the eqn f(x)=0 are 0.5,2 and k
    Let the cubic polynomial, f(x)=-2(x-0.5)(x-2)(x-k)

    Given that f(x) has a remainder -20 when divided by (x+2),
    f(-2)=-20
    -2(-2-0.5)(-2-2)(-2-k)=-20
    which gives k=-3
    Last edited by malaygoel; June 26th 2009 at 08:28 PM.
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  3. #3
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    Quote Originally Posted by helloying View Post


    the cubic polynomial is such that the coefficient of [tex]x^3[\math]is -2 ans the roots of the eqn f(x)=0 are 0.5,2 and k

    Given that f(x) has a remainder -20 when divided by (x+2), find the value of k.

    thank you

    .
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  4. #4
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    Quote Originally Posted by malaygoel View Post
    Let the cubic polynomial, f(x)=0.2(x-0.5)(x-2)(x-k)



    f(-2)=-20
    0.2(-2-0.5)(-2-2)(-2-k)=-20
    which gives k=8.

    shouldn't it be f(x)=-2(x-0.5)(x-2)(x-k) as the leading coefficient is -2 .
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  5. #5
    Super Member malaygoel's Avatar
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    Quote Originally Posted by mathaddict View Post
    shouldn't it be f(x)=-2(x-0.5)(x-2)(x-k) as the leading coefficient is -2 .
    I corrected it...thanks...see now...is it correct????
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  6. #6
    Member helloying's Avatar
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    thanks for your help. however i dont understand one thing. the qn mentioned that coefficent is -2 for x^3 but it did not mention for others.what if there are other coeficent for x^2 for something?will it have a differnet ans?

    And also kindly help me solve the 1st qn i asked. Thanks
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  7. #7
    Super Member malaygoel's Avatar
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    Quote Originally Posted by helloying View Post
    Find \int\sin^2 (3x+2) dx

    substitute 3x+2=t
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  8. #8
    Member helloying's Avatar
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    Quote Originally Posted by malaygoel View Post
    substitute 3x+2=t

    em i dont know how to intergete sin^2. can u teach me how to do?
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  9. #9
    Super Member Random Variable's Avatar
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    Quote Originally Posted by helloying View Post
    em i dont know how to intergete sin^2. can u teach me how to do?
     \sin^{2}u = \frac{1}{2} - \frac{\cos 2u}{2}
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