Let be defined on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

g(x)=\sin x

be defined on the interval

[0,2\pi]

. (a) Determine the average value of

g

[0,2\pi]

. (b) List all points

c

(0,2\pi)

for which

g(c)

equals this average value. (c) Verify that each value of

c

found in part (b) indeed lies in the open interval

(0,2\pi)