Given f(x)=1+2cos x , find the area under the curve y=f(x) between

Question

x = pi/2 and 2pi/3.

Answer 1

area = ∫ (1 + 2cosx) dx from x = π/2 to 2π/3
= [x + 2sinx] from π/2 to 2π/3

= (2π/3 + 2sin(2π/3) - (π/2 + 2sin(π/2)
= 2π/3 + 2(√3/2) - π/2 - 2(1)
= 2π/3 - π/2 + √3 - 2
simplify or express as needed
I get appr .2556
(unless I made an arithmetic error)