calculus

Find the area of the region using the method that requires you to evaluate just one integral.

Region between y=x and x+y=8 over [2,3]

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asked by George
  1. First graph the two functions to make sure that the required region is positive within the limits of integration.
    Let
    y1(x)=x
    y2(x)=8-x
    y1(2)=2, y1(3)=3
    y2(2)=6, y2(3)=5.
    Thus the region is always positive (the two function do not cross within the interval [2,3]).

    The incremental area is
    (y2(x)-y1(x))dx
    The area is thus the integral
    ∫(y2(x)-y1(x))dx between the limits 2 and 3.

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