2.  (Part 2 of the FTC in your book)  If f is continuous on [a, b] and F is an antiderivative of f on [a, b], then **F(b) – F(a) is often denoted as This part of the FTC is significant because it allows us to evaluate definite integrals.

3.  If f is continuous on [a, b] and then F’(x) = f(x) at every point x in [a, b]. You may also see this as

4.  Every continuous f is the derivative of some other function, namely  Every continuous function has an antiderivative.  The processes of integration and differentiation are inverses of each other!

5.  If, integrate to find F(x). Then, differentiate to find F’(x).

6.  Using FTC for, find F’(x).

7.  If, find h’(8).

8.  Find if (change bounds)

9.  Construct a function in the form of that has tan x as the derivative and satisfies f(3) = 5. andwhen x = 3, so

10.  Net area counts area below the x-axis as negative area.  Computing area on an entire interval using antiderivatives helps us find net area  Total area is the entire amount of area enclosed by a graph  Problems that say find “area” from here on out imply for you to find “total area.”

11. To find the area between the graph of y = f(x) and the x-axis over the interval [a, b] analytically, 1. Break [a, b] apart using the zeros of f 2. Integrate f over each subinterval 3. Add the absolute values of the integrals

12.  Find the area of the region between the curve y = 4 – x 2 and the x-axis over [0, 3]. 1.Break the curve into two subintervals since part of it is above the x-axis and the other is below. 2.Break the integral into [0, 2] and [2, 3] (subtract to make the second area positive)

13.  Find the net area of the region between the curve y = 4 – x 2 and the x-axis over [0, 3].

14.  To find the area between the graph of y = f(x) and the x-axis over the interval [a, b] numerically, evaluate