AP Calculus December 1, 2016 Mrs. Agnew

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Presentation transcript:

AP Calculus December 1, 2016 Mrs. Agnew The Definite Integral AP Calculus December 1, 2016 Mrs. Agnew

Essential Stuff Essential Question What are definite integrals and how do you evaluate them? Essential Vocabulary Riemann Sum Definite Integrals Antiderivative

Riemann Sums Used to find area under a curve… Divide interval in equal subintervals Draw rectangles with endpoints on curve (either left or right) or midpoints on curve Gives approximate area… more rectangles means better estimate. Calc in Motion Animation

The Definite Integral Riemann Sums The Definite Integral

The Definite Integral a and b are limits of integration (a is lower limit and b is upper limit) f(x) is integrand

The Definite Integral The definite integral is a number… it is the area under the curve between x = a and x = b. Area below the x-axis is negative since the y-coordinates (the heights of the rectangles) are negative.

Definite Integrals If a function f is continuous on the interval [a,b], then… where F is any antiderivative of f.

Practice and Homework Homework: page 278 – 281 Guided Practice Evaluate integrals given graph of function by interpreting in terms of area Use definite integral to find area under a curve (antidifferentiation) Use calculator to find area under a curve Homework: page 278 – 281 #15, 17, 21, 22, 25 – 31 (Odd), 45, 47 – 51