Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 5.1

1. What is the difference between signed area and area in the usual sense?
2. Translate $\int_{0}^{1}$x dx into English.
3. What does it mean to say that $\int_{1}^{4}$f (x) dx = - 2?
4. Draw the graph of a function f for which $\int_{1}^{4}$f (x) dx = - 2.
5. If $\int_{0}^{3}$g(x) dx = 4, what is $\int_{0}^{3}$4g(x) dx?
6. Explain the connection between the ``area under the curve'' meaning of integral and the ``average value'' meaning.
7. Suppose that f (t) represents the velocity of a car with t representing time. How would you interpret $\int_{0}^{2}$f (t) dt?
8. If $\int_{1}^{4}$f (x) dx = - 2, what is $\int_{4}^{1}$f (x) dx?