Evaluate the definite integral of y=1/cos ^2x. x=0 to x=pi/4

The definite integral will be evaluated using the
Leibniz-Newton formula.

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

We'll put 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 =
0:

F(0) = tan 0

F(0) =
0

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/4)
- F(0) 

Int dx/(cos x)^2 = 1 -
0

Int dx/(cos x)^2 = 1, from x = 0 to x =
pi/4