MAT 126: Exam 4
What are Reimann Sums? - ANS-It is a way to estimate the area beneath a curve.
Calculate the areas a rectangles, add them up, then multiply by the width of each
rectangle.
What is the fundamental theorem of calculus part 2? - ANS-If f is continuous on [a,b]
and F is an antiderivative of f on [a,b], then the finite integral from a to b of f(x) dx = F(b)
- F(a)
What is the fundamental theorem of calculus part 1? - ANS-If f is continuous on [a,b],
the area function A(x) = the finite integral from a to x of f(t) dt, a<x<b, is continuous on
[a,b], and differentiable on (a,b), then d/dx of the finite integral from a to x of f(t) dx = f(x)
How do you calculate the average value of a function? - ANS-See notes. On the domain
[a,b], the average value = 1/(a-b) x the finite integral between a and b for f(x).
When do you use u substitution? - ANS-There is not rule for integration for products,
quotients, or the chain rule. Instead, use u substitution.
How do you find the area of the region contained by multiple functions? - ANS-If f and g
are continuous, with f(x) greater than or equal to g(x) on [a,b], then the area of the
bounded region is the finite integral between a and b for (f(x) - g(x)). See notes.
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