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

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}}

Add a constant to the solution

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

\frac{d}{d x} (cos (\frac{π}{2} x))

\int_{- π}^{0} x d x

\int 2 e^{x^{2}} d x

2 x^{2} y^{^{'}} = y^{^{'}} + 4 x e^{- y}

x \to 0 lim (\frac{1}{2 x ^{2} + x})

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