# Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011.

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Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011

Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011

Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011

Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011 Arep i = (x i –x i 2 )xixi 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 x 2 to the x-axis. This is shown to the right.

Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011 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 –x 2 ) n  i=1

Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011 This defines the integral: A=  (x –x 2 ) Now we need to find the limits of integration by setting the two original functions together… x=x 2 …x=1…the first rectangle would set at x=0 and the last would set at x=1.

Created for ENMU Tutoring/Supplemental InstructionPeterson Fall 2011 Now integrate and evaluate the integral at the limits of integration. The answer should be 1/6.

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