Question

How do you use the second fundamental theorem of Calculus to find the derivative of given `int dt/(2+3sqrtt)` from `[0,x]`?

Answer 1

`d/dx int_0^x 1/(2 + 3sqrt t) \ dt = 1/(2 + 3sqrt x)`

Explanation:

By the 2nd FTC:

`d/dx int_a^x f(t) \ dt = f(x)`

So

`d/dx int_0^x 1/(2 + 3sqrt t) \ dt = 1/(2 + 3sqrt x)`

See Wolfram Mathworld