## Areas, Integrals, and Antiderivatives

Read this section to learn about the relationship among areas, integrals, and antiderivatives. Work through practice problems 1-5.

### Practice Answers

so (by The Area Function is an Antiderivative theorem): then and .

**Practice 2: **

(a) As an area, is the area of the triangular region between and the x– axis for .

(b) is an antiderivative of so area = .

**Practice 4: **

(b) In this problem we know the starting point is , and the total distance ("area") is 343 feet. Our problem is to find the time (Fig. 16) so .

**Practice 5:**

(a) number of new bacteria = .

(b) We know the total new population ("area" in Fig. 17) is 2875 – 1000 = 1875 so so