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Chapter 5 5.3 Definite Integrals Obj: find area using definite integrals
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Review Estimate the area using 4 subintervals between f(x)=x 3 and the x-axis from 0 to 2 using left and right sums.
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Riemann Sum Left Sum Right Sum Midpoint Sum Trapezoidal Sum
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Definite Integral If f is defined on the closed interval [a, b] and the limit exists, then If f is continuous on [a, b], then f is integrable on [a, b].
![Definite Integral If f is defined on the closed interval [a, b] and the limit exists, then If f is continuous on [a, b], then f is integrable on [a, b].](http://images.slideplayer.com/32/9805945/slides/slide_4.jpg "Definite Integral If f is defined on the closed interval [a, b] and the limit exists, then If f is continuous on [a, b], then f is integrable on [a, b].")
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Area IF f is continuous and nonnegative on the closed interval [a, b], then the area bounded by f, the x-axis and the vertical lines a and b is Area =
![Area IF f is continuous and nonnegative on the closed interval [a, b], then the area bounded by f, the x-axis and the vertical lines a and b is Area =](http://images.slideplayer.com/32/9805945/slides/slide_5.jpg "Area IF f is continuous and nonnegative on the closed interval [a, b], then the area bounded by f, the x-axis and the vertical lines a and b is Area =")
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Examples
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Rules 1.If f is defined at x = a,. 2.If f is integrable on [a, b], then 3.If c is on [a, b], then
![Rules 1.If f is defined at x = a,. 2.If f is integrable on [a, b], then 3.If c is on [a, b], then](http://images.slideplayer.com/32/9805945/slides/slide_7.jpg "Rules 1.If f is defined at x = a,. 2.If f is integrable on [a, b], then 3.If c is on [a, b], then")
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Assignment page 314 15 – 42 by 3, 47, 48
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