The function is defined for .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

The function

h(x)=2\sin x-1

is defined for

0\le x\le2\pi

. (a) Find all values of

x

[0,2\pi]

for which

h(x)=0

. (b) Compute the total area of the regions bounded by the graph of

h

and the

x

-axis over the interval

[0,2\pi]

. (c) Let

k(x)=|h(x)|

. Determine the average value of

k

on the interval

[0,2\pi]