Question

How do you use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function `int sqrt (2 + sec 7t)`?

Answer 1

Part 1 says:

`F(x) = intf(t)dt`

The derivative is the opposite of the indefinite integral, so:

`d/(dx)[intf(t)dt] = (cancel(d)cancel(F)^(f)(x))/cancel(dx) = f(x)`

`d/(dx)[intsqrt(2+sec7t)dt] = (dF(x))/(dx) = f(x) = sqrt(2+sec7x)`