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

The integral from-1 to 1 of 1/2 x^2 is 1/3

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

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

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{2}{3}

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

Simplify

= \frac{1}{3}

\frac{d y}{d x} = y (y^{2} - 1)

y = x^{2} + 2 x - 4

y = x^{3} + 3 x^{2}

\frac{\partial}{\partial x} (2 cos (y))

\frac{1}{5 x ^{2}}

What is the integral from-1 to 1 of 1/2 x^2 ?
The integral from-1 to 1 of 1/2 x^2 is 1/3