Question

Question #4eef0

Answer 1

`1+sec(sqrt(x))`

Explanation:

In a define integral where one of the limits is a variable it is poor notation to use the same variable as the variable of integration, so I will write

`int_pi^sqrt(x) \ sec(x)tan(x) \ dx` as `int_pi^sqrt(x) \ sec(t)tan(t) \ dt`

We use the known result

`d/dxsecx = secxtanx`

This gives us (without the need for a substitution):

`int_pi^sqrt(x) \ sec(t)tan(t) \ dt = [sect]_pi^sqrt(x)`
`" " = sec(sqrt(x)) - sec(pi)`
`" " = sec(sqrt(x)) - (-1)`
`" " = 1+sec(sqrt(x))`