What is the integral from-5 to 5 of 4(25-x^2) ?

The integral from-5 to 5 of 4(25-x^2) is 2000/3

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integral from-5 to 5 of 4(25-x^2)

\int_{- 5}^{5} 4 (25 - x^{2}) d x

\frac{2000}{3}

Decimal Notation

666.66666 \dots

Solution steps

\int_{- 5}^{5} 4 (25 - 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_{- 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

= 4 (\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}

= 4 (250 - \frac{250}{3})

Simplify

4 (250 - \frac{250}{3}) : \frac{2000}{3}

= \frac{2000}{3}

8 x - 5

\frac{d ^{4}}{d x ^{4}} (ln (1 + x))

y^{^{'}} + x = 0

\int 8 - 4 x - 4 x^{2} d x

x \to 0 lim (x^{2} + 4 x + 2)

What is the integral from-5 to 5 of 4(25-x^2) ?
The integral from-5 to 5 of 4(25-x^2) is 2000/3