7.1 Area of a Region Between Two Curves.

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Presentation transcript:

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)

A few notes If it is y in terms of “X”, subtract the lower from the upper curve. If is x in terms of “Y”, subtract the right curve from the left. Use the upper and lower values of “Y” for the values for integration

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

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)

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.

Now, set up the two integrals and solve.

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