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7.1 Area of a Region Between Two Curves

7.1 Area of a Region Between Two Curves. f. f. f. -. =. g. g. g. -. Area of region between f and g. Area of region under f(x). =. Area of region under g(x). Ex. Find the area of the region bounded by the graphs of f(x) = x 2 + 2, g(x) = -x, x = 0, and x = 1.

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7.1 Area of a Region Between Two Curves

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  1. 7.1 Area of a Region Between Two Curves

  2. f f f - = g g g - Area of region between f and g Area of region under f(x) = Area of region under g(x)

  3. Ex. Find the area of the region bounded by the graphs of f(x) = x2 + 2, g(x) = -x, x = 0, and x = 1 . Area = Top curve – bottom curve f(x) = x2 + 2 g(x) = -x

  4. Find the area of the region bounded by the graphs of f(x) = 2 – x2 and g(x) = x First, set f(x) = g(x) to find their points of intersection. 2 – x2 = x 0 = x2 + x - 2 0 = (x + 2)(x – 1) x = -2 and x = 1 fnInt(2 – x2 – x, x, -2, 1)

  5. Find the area of the region between the graphs of f(x) = 3x3 – x2 – 10x and g(x) = -x2 + 2x Again, set f(x) = g(x) to find their points of intersection. 3x3 – x2 – 10x = -x2 + 2x 3x3 – 12x = 0 3x(x2 – 4) = 0 x = 0 , -2 , 2 Note that the two graphs switch at the origin.

  6. Now, set up the two integrals and solve.

  7. Find the area of the region bounded by the graphs of x = 3 – y2 and y = x - 1 Area = Right - Left

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