What is the integral of (2sqrt(y)) ?

The integral of (2sqrt(y)) is 4/3 y^{3/2}+C

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integral of (2sqrt(y))

\int (2 y) d y

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

Solution steps

\int 2 y d y

Take the constant out:

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

= 2 \cdot \int y d y

Apply the Power Rule

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

= 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

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What is the integral of (2sqrt(y)) ?
The integral of (2sqrt(y)) is 4/3 y^{3/2}+C