1.
\(\displaystyle \int_0^2 f(x)\, dx\, dx\)
Print preview
Worksheet Some Exercises for this section
I included some practice problems that cover some main concepts in this section. You don’t need to turn it in, but I highly encourage you to work on this with your classmates. I may take problems here to be your in-class practice problems, homework problems, and/or exam problems. Reach out to Richard for help if you get stuck or have any questions.
I will only include the final answer to some of the problems for you to check your result. If you want to check your work, talk to Richard and he is happy to discuss the process with you.
Exercise Group.
2.
\(\displaystyle \int_0^5 f(x)\, dx\, dx\)
3.
\(\displaystyle \int_5^7 f(x)\, dx\, dx\)
4.
\(\displaystyle \int_0^9 f(x)\, dx\, dx\)
5.
Find the Rieman sum \(R(f,P,C)\) for \(f(x) = 2x + 3\text{,}\) \(P = \left\{-4, -1, 1, 4, 8\right\}\text{,}\) and \(C = \left\{-3, 0, 2, 5\right\}\text{.}\)
6.
Evaluate the definite integral \(\displaystyle \int_\pi^\pi \sin^2(x)\cos^4(x)\, dx\)
Exercise Group.
Given that
\begin{equation*}
\int_0^1 f(x)\, dx = 1, \qquad \int_0^2 f(x)\, dx = 4, \qquad \int_1^4 f(x)\, dx = 7
\end{equation*}
evaluate the following definite integrals.
7.
\(\displaystyle \int_0^4 f(x)\, dx\)
8.
\(\displaystyle \int_1^2 f(x)\, dx\)
9.
\(\displaystyle \int_4^1 f(x)\, dx\)
10.
\(\displaystyle \int_2^4 f(x)\, dx\)
11.
Justify grapically, with pretty pictures and explanation that
-
If \(g\) is a continuous even function, then \(\displaystyle \int_{-a}^a g(x)\, dx = 2\int_0^a g(x)\, dx\)
