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