What is the integral from 2 to 8 of-sqrt(x/2) ?

The integral from 2 to 8 of-sqrt(x/2) is -28/3

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integral from 2 to 8 of-sqrt(x/2)

\int_{2}^{8} - \frac{x}{2} d x

- \frac{28}{3}

Solution steps

\int_{2}^{8} - \frac{x}{2} d x

Take the constant out:

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

= - \int_{2}^{8} \frac{x}{2} d x

Simplify

\frac{x}{2} : \frac{x}{2}

= - \int_{2}^{8} \frac{x}{2} d x

Take the constant out:

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

= - \frac{1}{2} \cdot \int_{2}^{8} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{2}^{8}

= - \frac{1}{2} [\frac{2}{3} x^{\frac{3}{2}}]_{2}^{8}

Compute the boundaries:

\frac{28 2}{3}

= - \frac{1}{2} \cdot \frac{28 2}{3}

Simplify

= - \frac{28}{3}

\int \frac{cos ( ln ( 9 t ) )}{t} d t

\frac{d}{d x} (e^{2 c o s (3 x)})

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = - 9

y^{2} - 6 x = 1, x - y = 1

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

What is the integral from 2 to 8 of-sqrt(x/2) ?
The integral from 2 to 8 of-sqrt(x/2) is -28/3