What is the area of the region closed by the curve y=1/cos^2x, x axis and the lines x=pi/4 , x=pi/3?

To determine the area of he region bounded by the given
curve and lines, we'll have to compute the definite integral of
y.

This integral will be evaluated using the Leibniz-Newton
formula.

Int f(x)dx = F(b) - F(a), where x = a to x =
b

Let y = f(x) = 1/(cos
x)^2

We'll compute the indefinite integral,
first:

Int dx/(cos x)^2 = tan x +
C

We'll note the result F(x) = tan x +
C

We'll determine F(a), for a =
pi/3:

F(pi/3) = tan
pi/3

F(pi/3) = sqrt 3

We'll
determine F(b), for b = pi/4:

F(pi/4) = tan
pi/4

F(pi/4) = 1

We'll
evaluate the definite integral:

Int dx/(cos x)^2 = F(pi/3)
- F(pi/4)

Int dx/(cos x)^2 = sqrt 3 -
1

The area of the region, bounded by the
curve y=1/(cos x)^2, x axis and the lines x=pi/4 and x=pi/3, is: A = (sqrt 3 - 1) square
units.