Integration

Question

Find ∫√x dx


Answer
∫ x^1/3 dx

= x^1/3+1 /1/3+1 +c

 

Is this correct?

Answer 1

First, rewrite the integral using exponents.

 

∫x^1/2dx

 

 

Now use the power rule to integrate.

 

[x^{(1 + 1/2)} / (1 + 1/2)] + C =

 

[x^3/2 / (3/2)]  + C =

 

(2/3)x^3/2 + C

Answer 2

The antiderivative of THE SQUARE ROOT of x is ∫x^½dx =(2/3) x^(3/2) + C.

 

The antiderivative of THE CUBE ROOT  of x is (3/4)x^(4/3) + C.