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Definite Integral df. f continuous function on [a,b]. Divide [a,b] into n equal subintervals of width Let be a sample point. Then the definite integral of f from a to b is - Riemann sum. - number! If f(x) 0, then = area under the curve of y=f(x) from a to b. If f(x) positive and negative on [a,b], then where A 1 = area below y=f(x) and above axis x, A 2 = area below axis x and above y=f(x). y x 0 b a ++ -
![Definite Integral df. f continuous function on [a,b].](http://images.slideplayer.com/32/10057534/slides/slide_1.jpg "Divide [a,b] into n equal subintervals of width Let be a sample point. Then the definite integral of f from a to b is - Riemann sum. - number. If f(x) 0, then = area under the curve of y=f(x) from a to b. If f(x) positive and negative on [a,b], then where A 1 = area below y=f(x) and above axis x, A 2 = area below axis x and above y=f(x). y x 0 b a")
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Choose midpoint of the interval [x i-1, x i ] for integral approximation by Midpoint Rule: Properties of definite integrals
![Choose midpoint of the interval [x i-1, x i ] for integral approximation by Midpoint Rule: Properties of definite integrals](http://images.slideplayer.com/32/10057534/slides/slide_3.jpg "Choose midpoint of the interval [x i-1, x i ] for integral approximation by Midpoint Rule: Properties of definite integrals")
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y x 0 b a m M Fundamental Th of Calculus
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