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

The integral from 1 to 2 of 1/2 x^2 is 7/6

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integral from 1 to 2 of 1/2 x^2

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

\frac{7}{6}

Decimal

1.16666 \dots

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{2} x^{2} d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{7}{3}

= \frac{1}{2} \cdot \frac{7}{3}

Simplify

= \frac{7}{6}

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What is the integral from 1 to 2 of 1/2 x^2 ?
The integral from 1 to 2 of 1/2 x^2 is 7/6