Riemann Sums and Integrals

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Presentation transcript:

Riemann Sums and Integrals

The more rectangles I use, the closer my approximation will be to the exact area.

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

a) Write as a sum: heights ∆x = b – a n can be left/right/middle

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.

Antiderivatives

What is an Antiderivative?

Notation – Indefinite Integral Variable of Integration Constant of Integration Integrand Antiderivative of f(x)

Notation – Definite Integral Upper Bound Variable of Integration Evaluation Bar Lower Bound Integrand Antiderivative of f(x)