Question

How do you use the second fundamental theorem of Calculus to find the derivative of given `int sqrt(x^3-2x+6) dx` from `[-2, x^2]`?

Answer 1

Explained below

Explanation:

The second fundamental theorem says this

Now letting `x =t` the given integral becomes `int_2^(x^2) sqrt (t^3-2t+6) dt`

Accordingly `d/dx int_-2^(x^2) sqrt(t^3-2t+6)dt =2xsqrt(x^6-2x^2+6)` [Put t= `x^2` then `dt/dx` = 2x