What is the integral from 1 to 8 of 3sqrt(x) ?

The integral from 1 to 8 of 3sqrt(x) is 32sqrt(2)-2

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integral from 1 to 8 of 3sqrt(x)

\int_{1}^{8} 3 x d x

322 - 2

Decimal

43.25483 \dots

Solution steps

\int_{1}^{8} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{1}^{8} x d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{32 2}{3} - \frac{2}{3}

= 3 (\frac{32 2}{3} - \frac{2}{3})

Simplify

= 322 - 2

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What is the integral from 1 to 8 of 3sqrt(x) ?
The integral from 1 to 8 of 3sqrt(x) is 32sqrt(2)-2