What is the integral from 0 to 5 of 1/2 x^2 ?

The integral from 0 to 5 of 1/2 x^2 is 125/6

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integral from 0 to 5 of 1/2 x^2

\int_{0}^{5} \frac{1}{2} x^{2} d x

\frac{125}{6}

Decimal Notation

20.83333 \dots

Solution steps

\int_{0}^{5} \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_{0}^{5} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{5}

= \frac{1}{2} [\frac{x ^{3}}{3}]_{0}^{5}

Compute the boundaries:

\frac{125}{3}

= \frac{1}{2} \cdot \frac{125}{3}

Simplify

= \frac{125}{6}

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\int_{0}^{1} (a + x)^{2} - x^{2} d a

What is the integral from 0 to 5 of 1/2 x^2 ?
The integral from 0 to 5 of 1/2 x^2 is 125/6