Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 6.1

1. What does the Fundamental Theorem of Calculus say, in your own words?
2. Use the FTC to figure out $\int_{1}^{4}$x² dx.
3. What's a definite integral? Indefinite?
4. What does Newton's inverse-square law (p. 400) mean?
5. Why is antidifferentiation harder? What's the general strategy for finding antiderivatives?
6. Evaluate (compute) $\int_{-\pi/2}^{\pi/2}$cos(kx)dx, where k is some nonzero integer.
7. Since $\int$sinx dx = - cos x + C and $\int$3 dx = 3x + C, does this mean that $\int$(sinx + 3)dx = - cos x + 3x + C and $\int$3sinx dx = - 3xcos x + C?
8. Explain again where the C in the solution to an integral comes from?