Does anyone know what the antiderivative of the square root of X - 1 is?

Question

this is for AP Calc.... and I got (2/3) X^ (3/2) - x.... but apparently thats wrong.. or is it?

well the full problem is find the area btw the curve and the x acis for f(x) = Sqrt[x]- 1 on [0,4]. so i understand that i have to fine the ∫ from 0 to 4 of the function... does anyone know the final answer?

well the full problem is find the area btw the curve and the x acis for f(x) = Sqrt[x]- 1 on [0,4]. so i understand that i have to fine the ∫ from 0 to 4 of the function... does anyone know the final answer?

Answer 1

Start with the equation as given: sqrt(x-1). Let's represent this as (x-1)^1/2. To integrate, follow the power rule.

integral (x-1)^1/2 = 2/3(x-1)^3/2.

The problem looks different if it's sqrt(x)-1 or (x^1/2)-1

integral (x^1/2)-1 = (2/3x^3/2) - x.

Answer 2

(x-1) x (1-x)