What is the integral from-5 to 1 of 1/6 (5-4x-x^2) ?

The integral from-5 to 1 of 1/6 (5-4x-x^2) is 6

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integral from-5 to 1 of 1/6 (5-4x-x^2)

\int_{- 5}^{1} \frac{1}{6} (5 - 4 x - x^{2}) d x

6

Solution steps

\int_{- 5}^{1} \frac{1}{6} (5 - 4 x - x^{2}) d x

Take the constant out:

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

= \frac{1}{6} \cdot \int_{- 5}^{1} 5 - 4 x - 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}{6} (\int_{- 5}^{1} 5 d x - \int_{- 5}^{1} 4 x d x - \int_{- 5}^{1} x^{2} d x)

\int_{- 5}^{1} 5 d x = 30

\int_{- 5}^{1} 4 x d x = - 48

\int_{- 5}^{1} x^{2} d x = 42

= \frac{1}{6} (30 - (- 48) - 42)

Simplify

\frac{1}{6} (30 - (- 48) - 42) : 6

= 6

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What is the integral from-5 to 1 of 1/6 (5-4x-x^2) ?
The integral from-5 to 1 of 1/6 (5-4x-x^2) is 6