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    help with integration question?

    can anyone help me with the process to the question. points i need to research rather than the answers. many thanks

    The function y=2(x-1)(x-4)^2

    (a) find the values of A and B
    (b) what is the size of the shaded part


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  2. #2
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    Quote Originally Posted by decoy808 View Post
    can anyone help me with the process to the question. points i need to research rather than the answers. many thanks

    The function y=2(x-1)(x-4)^2

    (a) find the values of A and B
    (b) what is the size of the shaded part



    should be clear that A = 1 and B = 4 (roots of the cubic, one w/ multiplicity two)

    area = \int_1^4 2(x-1)(x-4)^2 \, dx

    expand the cubic, then integrate and evaluate the definite integral using the fundamental theorem of calculus.
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    <br /> <br />

    A and B occur when y=0

    y=2(x-1)(x-4)^2
    0=2(x-1)(x-4)^2


    <br />
0=(x-1) and 0=(x-4)

    Therefore...
    A=1 and B=4


    The Area is..
    \int2(x-1)(x-4)^2dx
    2\int(x-1)(x^2-8x+16)dx
    2\int(x^3-7x^2+24x-16)dx

    Limits of integration are 1 to 4
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