What is the integral from 0 to 25 of 4sqrt(x) ?

The integral from 0 to 25 of 4sqrt(x) is 1000/3

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integral from 0 to 25 of 4sqrt(x)

\int_{0}^{25} 4 x d x

\frac{1000}{3}

Decimal

333.33333 \dots

Solution steps

\int_{0}^{25} 4 x d x

Take the constant out:

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

= 4 \cdot \int_{0}^{25} x d x

Apply the Power Rule

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

= 4 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{25}

Compute the boundaries:

\frac{250}{3}

= 4 \cdot \frac{250}{3}

Simplify

= \frac{1000}{3}

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What is the integral from 0 to 25 of 4sqrt(x) ?
The integral from 0 to 25 of 4sqrt(x) is 1000/3