The Definite Integral
Learning Objectives
- Riemann Sums
- Net area
- Properties of the definite integral
Concept Video(s)
Exercises
1.
\(28 + \dfrac{9}{2} \pi\,\) units\(^2\)
2.
80
3.
80
4.
88
5.
10.4
6.
\(\displaystyle{\int^{-3}_{-8} f(x) \ dx} = 0\)
7.
\(\displaystyle{\int^{2}_{-1} f(x) \ dx}=-7\)
8.
\(-12\leq \displaystyle{\int^3_{-1} -x \hspace{0.2cm}dx} \leq \displaystyle{\int^3_{-1}(10-x^2) \hspace{0.2cm} dx}\leq 40\)
\(4 \leq \displaystyle{\int^3_{-1}(10-x^2) \hspace{0.2cm} dx}\leq 40\)
\(-12 \leq \displaystyle{\int^3_{-1} -x \hspace{0.2cm}dx} \leq 4\)
\(4 \leq \displaystyle{\int^3_{-1}(10-x^2) \hspace{0.2cm} dx}\leq 40\)
\(-12 \leq \displaystyle{\int^3_{-1} -x \hspace{0.2cm}dx} \leq 4\)