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Riemann Sums and Integrals
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The more rectangles I use, the closer my approximation will be to the exact area.
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Definite Integral The Definite Integral is the limit of a Riemann Sum
Can be used to find area Definite Integral is about summing things up
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a) Write as a sum: heights ∆x = b – a n can be left/right/middle
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Note that ∆x is no longer ½ because we now have infinite rectangles, not only 4. So, ∆x= = tiny # dx is the tiny width of each rectangle. Each rectangle is infinitesimally thin.
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Antiderivatives
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What is an Antiderivative?
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Notation – Indefinite Integral
Variable of Integration Constant of Integration Integrand Antiderivative of f(x)
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Notation – Definite Integral
Upper Bound Variable of Integration Evaluation Bar Lower Bound Integrand Antiderivative of f(x)
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