Find the area of the region bounded above by y=2cosx and above by y=secx,-π/4≤x≤π/4

Answer 1

Assuming you meant the region below y= 2cos(x) and above y=sec(x):

Area = int (-π/4)^(π/4) (2cos(x) - sec(x)) dx
= (-π/4)^(π/4) [2sin(x) - ln|sec(x) +tan(x)| ]
=[2sin(π/4) - ln|sec(π/4) +tan(π/4)|] - [2sin(-π/4) - ln|sec(-π/4) +tan(-π/4)|]
= ________