Question

How do you use the Fundamental Theorem of Calculus to find the derivative of `int sqrt (2 + sec 7t)` from x to pi?

Answer 1

`= - sqrt (2 + sec 7x)`

Explanation:

`d/dx int_x^pi sqrt (2 + sec 7t) \ dt qquad star`

by FTC part 2, `d/dx int_a^x \ f(t) \ dt = f(x)`

so `star` becomes

`- d/dx int_pi^x sqrt (2 + sec 7t) \ dt`

`= - sqrt (2 + sec 7x)`