What is the integral from 0 to 1 of (x^2)/2 ?

The integral from 0 to 1 of (x^2)/2 is 1/6

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integral from 0 to 1 of (x^2)/2

\int_{0}^{1} \frac{x ^{2}}{2} d x

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

\int_{0}^{1} \frac{x ^{2}}{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_{0}^{1} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{1}

= \frac{1}{2} [\frac{x ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

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

Simplify

= \frac{1}{6}

\int_{- 3}^{1} \frac{1}{x ^{4}} d x

\int_{0}^{4} x x^{2} + 5 d x

\int_{- 1}^{1} 3 x^{5} d x

\int_{0}^{\frac{π}{2}} x sin^{2} (x) d x

\int_{- 1}^{1} 3 x^{3} - x^{2} + x - 1 d x

What is the integral from 0 to 1 of (x^2)/2 ?
The integral from 0 to 1 of (x^2)/2 is 1/6