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Math Help - How to find the area enclosed by two curves?

  1. #1
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    Question How to find the area enclosed by two curves?

    f(x) = 2x - x

    g(x) = 3 - 2x


    how do i find the area enclosed by two graphs?

    thanks in advance!
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  2. #2
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    Quote Originally Posted by da_coolest View Post
    f(x) = 2x - x

    g(x) = 3 - 2x


    how do i find the area enclosed by two graphs?

    thanks in advance!
    \int ^a_b f(x) - \int ^a_b g(x)

    the limits are the points where the two lines intersect

    In this case:

    2x-x^2  = 3-2x^2 \: , \: x^2+2x-3=0

    Solve the quadratic to give x = 1, -3

    \int ^1_{-3} (2x-x^2)dx - \int ^1_{-3} (3-2x^2) dx

    If your answer is negative then ignore the minus sign/take the absolute value - it just means you took the smaller curve from the higher one
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