What is the integral from 0 to 5 of kx^{3/2} ?

The integral from 0 to 5 of kx^{3/2} is k*10*5^{1/2}

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integral from 0 to 5 of kx^{3/2}

\int_{0}^{5} k x^{\frac{3}{2}} d x

k \cdot 10 \cdot 5^{\frac{1}{2}}

Solution steps

\int_{0}^{5} k x^{\frac{3}{2}} d x

Take the constant out:

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

= k \cdot \int_{0}^{5} x^{\frac{3}{2}} d x

Apply the Power Rule

: [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{5}

= k [\frac{2}{5} x^{\frac{5}{2}}]_{0}^{5}

Compute the boundaries:

10 \cdot 5^{\frac{1}{2}}

= k \cdot 10 \cdot 5^{\frac{1}{2}}

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What is the integral from 0 to 5 of kx^{3/2} ?
The integral from 0 to 5 of kx^{3/2} is k*10*5^{1/2}