Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 5.3

1. Again: What does the Fundamental Theorem of Calculus say, in your own words?
2. Why are the original function f and ``the area under the curve of f' between 0 and x'' the same?
3. Which is harder to find, derivatives or antiderivatives? Why?
4. If you can find one antiderivative of a function, how do you find all the others?
5. What is an antiderivative of f (x) = x³? What's another one?
6. What is the area under the graph of f (x) = x³ between x = 1 and x = 2? Does it matter which of the antiderivatives you use to figure this out? Why or why not?
7. What does $\left.\vphantom{ x^2}\right.$x²$\left.\vphantom{ x^2}\right]_{0}^{1}$ mean?
8. If f (t) represents the velocity of a car at time t, what does $\int_{1}^{3}$f (x) dx represent?
9. What does $\int$g(x) dx represent?