What is the integral from 0 to 25 of (-6sqrt(x)) ?

The integral from 0 to 25 of (-6sqrt(x)) is -500

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integral from 0 to 25 of (-6sqrt(x))

\int_{0}^{25} (- 6 x) d x

- 500

Solution steps

\int_{0}^{25} - 6 x d x

Take the constant out:

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

= - 6 \cdot \int_{0}^{25} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{25}

= - 6 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{25}

Compute the boundaries:

\frac{250}{3}

= - 6 \cdot \frac{250}{3}

Simplify

= - 500

x \to 2 lim (x^{3} - 5 x^{2} + 1)

\int_{0}^{2} (x + y) d y

\frac{1}{8 x}

\frac{d}{d x} (ln (e^{- 2 x} + cos (x)))

\frac{d}{d x} (sin^{3} (3 x^{2} + 6 x))

What is the integral from 0 to 25 of (-6sqrt(x)) ?
The integral from 0 to 25 of (-6sqrt(x)) is -500