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Calculus II- Finding Area between curves By: Kristilyn Peterson

Calculus II- Finding Area between curves By: Kristilyn Peterson. The problem we will solve will be: Find the area between y= x 2 and y=x to the right of the origin. (they can give you a interval but we can find it!). First draw a CLEAR picture. The area of the rectangle is

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Calculus II- Finding Area between curves By: Kristilyn Peterson

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  1. Calculus II- Finding Area between curves By: Kristilyn Peterson

  2. The problem we will solve will be: Find the area between y= x2 and y=x to the right of the origin. (they can give you a interval but we can find it!)

  3. First draw a CLEAR picture

  4. The area of the rectangle is L x W. The width is the change in the x direction (delta x) and the length is the point on the function y=x to the x-axis minus the point on x2 to the x-axis. This is shown to the right. Arepi = (xi –xi2) xi • Second draw and find area of the representative “rectangle”

  5. Now we need to form the Riemann sum because we are going to fill this area with little rectangle and take the limit as the number approaches infinity. • n • lim(x –x2) • n i=1

  6. This defines the integral: A=(x –x2) Now we need to find the limits of integration by setting the two original functions together… x=x2 …x=1…the first rectangle would set at x=0 and the last would set at x=1.

  7. Now integrate and evaluate the integral at the limits of integration. • The answer should be 1/6 .

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