Let on the interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

g(x)=|\sin x|

on the interval

0\le x\le 2\pi

. (i) Express

g(x)

as a piecewise‐defined function without the absolute value sign over the interval

0\le x\le 2\pi

. (ii) Obtain a single antiderivative

G(x)

that is valid for all

x

[0,2\pi]

by integrating each piece and stitching the results together so that

G(x)

is continuous on the whole interval. (iii) Using the antiderivative found in part (ii), compute

G(2\pi)-G(0)

without re‐integrating.