Problem 1
T/F: Simpson's Rule is a method of approximating antiderivatives.
Problem 1
Define the term "antiderivative" in your own words.
Problem 1
How are definite and indefinite integrals related?
Problem 2
What are the two basic situations where approximating the value of a definite integral is necessary?
Problem 2
What is the upper bound in the summation \(\sum_{i=7}^{14}(48 i-201) ?\)
Problem 2
Is it more accurate to refer to "the" antiderivative of \(f(x)\) or "an" antiderivative of \(f(x)\) ?
Problem 3
What is \(\int_{3}^{3} \sin x d x ?\)
Problem 3
\(\mathrm{T} / \mathrm{F}:\) If \(f\) is a continuous function, then \(F(x)=\int_{a}^{x} f(t) d t\) is also a continuous function.
Problem 4
Simpson's Rule is based on approximating portions of a function with what type of function?
Problem 4
The definite integral can be used to find "the area under a curve." Give two other uses for definite integrals.
