what the antiderivative of this?

Question

the square root of x

Answer 1

(2/3)*x^(3/2) + C, where C is a constant

Answer 2

V means square root:

Vx= x^1/2

x-1= 1/2, x= 3/2

(y)(3/2)=1, y=2/3

therefore the antiderivative of Vx= (2/3)(x^3/2) + C

*As I said before C is merely to signify a constant

Answer 3

So you want to find

Integral (sqrt(x))dx

This is the same as

Integral (x^(1/2)) dx

And we just use the reverse power rule. The antiderivative of x^n is [x^(n+1)]/(n+1)

So the integral of x^(1/2) is

[x^(1/2 + 1)]/[1/2 + 1], or
[x^(3/2)]/[3/2), or

(2/3) x^(3/2)

Answer 4

on antiderivatives you add one to the power then divide by the newpower so:

antiderivative x^1/2 = 2x^(3/2)/3