What is the integral from 0 to 10 of 1.5sqrt(x) ?

The integral from 0 to 10 of 1.5sqrt(x) is 31.62277…

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integral from 0 to 10 of 1.5sqrt(x)

\int_{0}^{10} 1.5 x d x

31.62277 \dots

Solution steps

\int_{0}^{10} 1.5 x d x

Take the constant out:

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

= 1.5 \cdot \int_{0}^{10} x d x

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{10}

= 1.5 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{10}

Simplify

= 1.5 [0.66666 \dots x^{\frac{3}{2}}]_{0}^{10}

Compute the boundaries:

21.08185 \dots

= 1.5 \cdot 21.08185 \dots

Simplify

= 31.62277 \dots

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What is the integral from 0 to 10 of 1.5sqrt(x) ?
The integral from 0 to 10 of 1.5sqrt(x) is 31.62277…