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

The integral from-2 to 2 of 1/2 (4^2-x^4) is 128/5

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

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

\frac{128}{5}

Decimal

25.6

Solution steps

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

Simplify

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

\int_{- 2}^{2} 16 d x = 64

\int_{- 2}^{2} x^{4} d x = \frac{64}{5}

= \frac{1}{2} (64 - \frac{64}{5})

Simplify

\frac{1}{2} (64 - \frac{64}{5}) : \frac{128}{5}

= \frac{128}{5}

\int_{0}^{1} 1 + 3 x d x

y = - 4 x - 3 y = - 4 x - 3

\int_{0}^{3} π (\frac{2}{3} x)^{2} d x

- 3 sin (3 t)

\frac{d}{d x} (sin^{- 2} (x))

What is the integral from-2 to 2 of 1/2 (4^2-x^4) ?
The integral from-2 to 2 of 1/2 (4^2-x^4) is 128/5