Question

How do you evaluate the definite integral `int sec^2x` from `[-pi/6, pi/6]`?

Answer 1

`2/sqrt3`

Explanation:

`int_(- pi/6)^(pi/6) sec^2 x dx`

the integral of this well known differential....
`= int_(- pi/6)^(pi/6) d/dx (tan x) dx`

..... is the differential itself
`= [tan x ]_(- pi/6)^(pi/6) = 2/sqrt3`