What is the integral from 1 to 2 of x^{3/2} ?

The integral from 1 to 2 of x^{3/2} is (8*2^{1/2}-2)/5

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integral from 1 to 2 of x^{3/2}

\int_{1}^{2} x^{\frac{3}{2}} d x

\frac{8 \cdot 2 ^{\frac{1}{2}} - 2}{5}

Decimal

1.86274 \dots

Solution steps

\int_{1}^{2} x^{\frac{3}{2}} d x

Apply the Power Rule

= [\frac{2}{5} x^{\frac{5}{2}}]_{1}^{2}

Compute the boundaries:

\frac{8 \cdot 2 ^{\frac{1}{2}}}{5} - \frac{2}{5}

= \frac{8 \cdot 2 ^{\frac{1}{2}}}{5} - \frac{2}{5}

Simplify

= \frac{8 \cdot 2 ^{\frac{1}{2}} - 2}{5}

What is the integral from 1 to 2 of x^{3/2} ?
The integral from 1 to 2 of x^{3/2} is (8*2^{1/2}-2)/5