Consider the function on the interval .

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

Consider the function

g(x)=2\cos(3x)+3

on the interval

0\le x\le \dfrac{\pi}{6}

. (a) Verify that

g(x)

is non-negative on the given interval. (b) Determine the exact area of the region bounded above by the graph of

g

and below by the

x

-axis between

x=0

and

x=\dfrac{\pi}{6}

. Show all work leading to your result. (c) State the average value of

g

on this interval and explain how it relates to the area you found in part (b).