Let f be a function that is continuous on the closed interval [a, b]. The definite integral of f from a and b is defined to be the limit
is a Riemann Sum of f is [a, b]
We assume that f and g are continuous functions.
Given that , evaluate
Approximating Area Using Rectangles
When finding the area under a curve for a region, it is often easiest to approximate area using a summation series. This approximation is a summation of areas of rectangles. The rectangles can be either left-handed or right-handed and, depending on the concavity, will either overestimate or underestimate the true area.
Approximating a Definite Integral Using Rectangles
This video shows how to use 4 rectangles and left endpoints as well as midpoints to approximate the area underneath 16 - x2 from x = 0 to x = 2.
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