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Wednesday, April 20, 2016MAT 145. Wednesday, April 20, 2016MAT 145.

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Presentation on theme: "Wednesday, April 20, 2016MAT 145. Wednesday, April 20, 2016MAT 145."— Presentation transcript:

1 Wednesday, April 20, 2016MAT 145

2 Wednesday, April 20, 2016MAT 145

3 Wednesday, April 20, 2016MAT 145

4 Wednesday, April 20, 2016MAT 145 Riemann Sum Applet

5 Wednesday, April 20, 2016MAT 145 The first three methods build RECTANGLES on each subinterval and the fourth builds TRAPEZOIDS on each subinterval. In all cases, the lowercase letter k indicates the number of subintervals.

6 Wednesday, April 20, 2016MAT 145 Here is the velocity graph of a braking car. How far did the car travel during this 6-second brake application?

7 Wednesday, April 20, 2016MAT 145 Let g(x) = sin(x). Show a calculator graph of g(x) using window dimensions of [-1,4] on x and [-1.25,1.25] on y. Now calculate. Label your antiderivative G(x). Next, evaluate your antiderivative, G(x), when x = π and when x = π / 2. Finally, calculate G(π) – G( π / 2 ).

8 Wednesday, April 20, 2016MAT 145 This is called a definite integral. It includes lower bounds and upper bounds that represent boundary values of an x-axis interval. upper limit of integration lower limit of integration integrand differential

9 Wednesday, April 20, 2016MAT 145 Use the graph of y = f(x) shown here to express the value of each integral in terms of accumulated area.

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