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Thread: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation please!!!

  1. #1
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    Help with leaving integratio in the form a+bsqrt3 and simultaneous equation please!!!

    1.Find the values of p and q which satisfy the following simultaneous equations
    ∫from2to1(px^2 + q) dx = 9
    ∫from2to1 (qx + p) dx = 6



    2a) Expand (4sqrtx + 3)^2 DONE 16x + 24sqrtx + 9.

    b) Hence evaluate
    ∫from3to0 (4sqrtx + 3)^2 dx

    Giving your answer in the form a + bsqrt3 where a and b are integers.


    Thanks!
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  2. #2
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    Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

    Quote Originally Posted by shan View Post
    1.Find the values of p and q which satisfy the following simultaneous equations
    ∫from2to1(px^2 + q) dx = 9
    ∫from2to1 (qx + p) dx = 6



    2a) Expand (4sqrtx + 3)^2 DONE 16x + 24sqrtx + 9.

    b) Hence evaluate
    ∫from3to0 (4sqrtx + 3)^2 dx

    Giving your answer in the form a + bsqrt3 where a and b are integers.
    Are you asking for someone else to do your work for you?
    Thanks from topsquark
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  3. #3
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    Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

    I have come across 2 questions that I am really struggling to answer and I would like to know how they are done?
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  4. #4
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    Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

    Quote Originally Posted by shan View Post
    I have come across 2 questions that I am really struggling to answer and I would like to know how they are done?
    If you are saying that you do not know how to evaluate $\int_1^2 {(qx + p)dx}$, then you need more instruction than we can give you.
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  5. #5
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    Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

    This was posted in the "algebra" forum. Perhaps shan has never taken a Calculus class and stumbled onto this problem by accident!
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    Re: Help with leaving integratio in the form a+bsqrt3 and simultaneous equation pleas

    Quote Originally Posted by shan View Post
    1.Find the values of p and q which satisfy the following simultaneous equations
    ∫from2to1(px^2 + q) dx = 9
    ∫from2to1 (qx + p) dx = 6
    If you have taken Calculus then you should know that the first equation is (p/3)x^3+ qx= 9 and the second (q/3)x^3+ px= 6.
    Multiplying the first equation by q and the second by p, you have (pq/3)x^3+ q^2x= 9q and (pq/3)x^3+ p^3x= 6p. Subtracting (p^2- q^2)x= 6p- 9q.



    2) Expand (4sqrtx + 3)^2 DONE 16x + 24sqrtx + 9.

    b) Hence evaluate
    ∫from3to0 (4sqrtx + 3)^2 dx[tex]

    Giving your answer in the form a + bsqrt3 where a and b are integers.


    Thanks!
    sqrt(x) is the same as x^(1/2) so you are being asked to integrate 16x+ 24x^(1/2)+ 9 with respect to x. Again, the integral of x^n is (1/(n+1))x^(n+1). The integral of 16x= 16x^1 is (1/2)x^2= 8x^2 and the integral of 24x^(1/2) is 24(2/3)x^(3/2)= 16x^(3/2). The integral of 9= 9x^0 is 9x.
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