Mathematics

Problem

Consider the function

g(x)=5\sin(2x)+3

defined on

[0,\pi]

. a. Part 1: (a) Compute the average value of

g

[0,\pi]

. b. Part 2: (b) Solve the equation

g(c) = (\text{average value from part (a)})

for all

c

[0,\pi]

. Express exact solutions and then provide decimal approximations correct to three decimal places.