What is the integral of 2y^{1/2} ?

The integral of 2y^{1/2} is 4/3 y^{3/2}+C

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integral of 2y^{1/2}

\int 2 y^{\frac{1}{2}} d y

\frac{4}{3} y^{\frac{3}{2}} + C

Solution steps

\int 2 y^{\frac{1}{2}} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int y^{\frac{1}{2}} d y

Apply the Power Rule

= 2 \cdot \frac{2}{3} y^{\frac{3}{2}}

Simplify

2 \cdot \frac{2}{3} y^{\frac{3}{2}} : \frac{4}{3} y^{\frac{3}{2}}

= \frac{4}{3} y^{\frac{3}{2}}

Add a constant to the solution

= \frac{4}{3} y^{\frac{3}{2}} + C