What is the integral from-4 to 4 of 1/2 (16-x^2) ?

The integral from-4 to 4 of 1/2 (16-x^2) is 128/3

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integral from-4 to 4 of 1/2 (16-x^2)

\int_{- 4}^{4} \frac{1}{2} (16 - x^{2}) d x

\frac{128}{3}

Decimal Notation

42.66666 \dots

Solution steps

\int_{- 4}^{4} \frac{1}{2} (16 - 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_{- 4}^{4} 16 - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{- 4}^{4} 16 d x - \int_{- 4}^{4} x^{2} d x)

\int_{- 4}^{4} 16 d x = 128

\int_{- 4}^{4} x^{2} d x = \frac{128}{3}

= \frac{1}{2} (128 - \frac{128}{3})

Simplify

\frac{1}{2} (128 - \frac{128}{3}) : \frac{128}{3}

= \frac{128}{3}

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What is the integral from-4 to 4 of 1/2 (16-x^2) ?
The integral from-4 to 4 of 1/2 (16-x^2) is 128/3