Question

Question #299c9

Answer 1

The expression is undefined.

(A problem with similar structure linked here)

Explanation:

Simplify the trig terms by imagining the unit circle, or breaking the terms down into `sin` and `cos`:

`ln(sec(pi/2)+tan(pi/2))-ln(sec0+tan0)`

`=ln(1/cos(pi/2) + sin(pi/2)/cos(pi/2))-ln(1+0)`

We know `ln1=0` because of the properties of logarithms
`=ln(frac{1+sin(pi/2)}{cos(pi/2)})-0`

`=ln(frac{2}{cos(pi/2)})`

Since `cos (pi/2) = 0` is in the denominator of the fraction inside the natural log, the expression is undefined.

---

Separately however, if this problem started out as `int_0^(pi/2) (secx)dx`, then click here to look at the solution to the improper integral.