Question

How do you use the second fundamental theorem of Calculus to find the derivative of given `int sqrt((t^3)+1)` from `[-1, x]`?

Answer 1

`sqrt((x^3)+1)`

Explanation:

FTC part 1 tells us that

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

so `d/dx( int_(-1)^x sqrt((t^3)+1) dt )`

`sqrt((x^3)+1)`