What is the integral of (-2x^{1/2}) ?

The integral of (-2x^{1/2}) is -4/3 x^{3/2}+C

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integral of (-2x^{1/2})

\int (- 2 x^{\frac{1}{2}}) d x

- \frac{4}{3} x^{\frac{3}{2}} + C

Solution steps

\int - 2 x^{\frac{1}{2}} d x

Take the constant out:

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

= - 2 \cdot \int x^{\frac{1}{2}} d x

Apply the Power Rule

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

= - 2 \cdot \frac{2}{3} x^{\frac{3}{2}}

Simplify

- 2 \cdot \frac{2}{3} x^{\frac{3}{2}} : - \frac{4}{3} x^{\frac{3}{2}}

= - \frac{4}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - \frac{4}{3} x^{\frac{3}{2}} + C

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What is the integral of (-2x^{1/2}) ?
The integral of (-2x^{1/2}) is -4/3 x^{3/2}+C