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

The integral from-4 to 4 of 4(16-x^2) is 1024/3

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

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

\frac{1024}{3}

Decimal Notation

341.33333 \dots

Solution steps

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

Take the constant out:

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

= 4 \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

= 4 (\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}

= 4 (128 - \frac{128}{3})

Simplify

4 (128 - \frac{128}{3}) : \frac{1024}{3}

= \frac{1024}{3}

2 x^{3} - 5

x \to - 1 - lim (\frac{1}{x - 1} + e^{x})

\frac{d}{d t} (3 t)

\int \frac{( x ^{2} + 2 x + 1 )}{( x + 3 )} d x

\frac{d y}{d t} = y^{2} - 4

What is the integral from-4 to 4 of 4(16-x^2) ?
The integral from-4 to 4 of 4(16-x^2) is 1024/3