What is the integral from-5 to 5 of 1/2 (25-x^2) ?

The integral from-5 to 5 of 1/2 (25-x^2) is 250/3

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integral from-5 to 5 of 1/2 (25-x^2)

\int_{- 5}^{5} \frac{1}{2} (25 - x^{2}) d x

\frac{250}{3}

Decimal Notation

83.33333 \dots

Solution steps

\int_{- 5}^{5} \frac{1}{2} (25 - 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_{- 5}^{5} 25 - 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_{- 5}^{5} 25 d x - \int_{- 5}^{5} x^{2} d x)

\int_{- 5}^{5} 25 d x = 250

\int_{- 5}^{5} x^{2} d x = \frac{250}{3}

= \frac{1}{2} (250 - \frac{250}{3})

Simplify

\frac{1}{2} (250 - \frac{250}{3}) : \frac{250}{3}

= \frac{250}{3}

(6 x + 1) y^{2} \frac{d y}{d x} + 4 x^{2} + 2 y^{3} = 0

y = \frac{x ^{2}}{x + 5}, (1, \frac{1}{6})

\frac{\partial}{\partial x} (\frac{1}{x} + \frac{1}{y + z})

\frac{\partial}{\partial x} (y x^{2} z^{2} - x y^{4} + x z)

\frac{d}{d x} ((3 x^{2} + 5 x + 1)^{\frac{3}{2}})

What is the integral from-5 to 5 of 1/2 (25-x^2) ?
The integral from-5 to 5 of 1/2 (25-x^2) is 250/3