What is the integral of-sqrt(2-x) ?

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

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integral of-sqrt(2-x)

\int - 2 - x d x

\frac{2}{3} (2 - x)^{\frac{3}{2}} + C

Solution steps

\int - 2 - x d x

Take the constant out:

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

= - \int 2 - x d x

Apply u-substitution

: \int - u d u

= - \int - u d u

Take the constant out:

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

= - (- \int u d u)

Apply the Power Rule

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

= - (- \frac{2}{3} u^{\frac{3}{2}})

Substitute back

u = 2 - x

= - (- \frac{2}{3} (2 - x)^{\frac{3}{2}})

Simplify

= \frac{2}{3} (2 - x)^{\frac{3}{2}}

Add a constant to the solution

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

f (x) = 4 - x, x = - 2, x = 6, x

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