What is the integral from 2 to 6 of-(x^2-7x+6) ?

The integral from 2 to 6 of-(x^2-7x+6) is 56/3

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integral from 2 to 6 of-(x^2-7x+6)

\int_{2}^{6} - (x^{2} - 7 x + 6) d x

\frac{56}{3}

Decimal Notation

18.66666 \dots

Solution steps

\int_{2}^{6} - (x^{2} - 7 x + 6) d x

Take the constant out:

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

= - \int_{2}^{6} x^{2} - 7 x + 6 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

= - (\int_{2}^{6} x^{2} d x - \int_{2}^{6} 7 x d x + \int_{2}^{6} 6 d x)

\int_{2}^{6} x^{2} d x = \frac{208}{3}

\int_{2}^{6} 7 x d x = 112

\int_{2}^{6} 6 d x = 24

= - (\frac{208}{3} - 112 + 24)

Simplify

- (\frac{208}{3} - 112 + 24) : \frac{56}{3}

= \frac{56}{3}

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What is the integral from 2 to 6 of-(x^2-7x+6) ?
The integral from 2 to 6 of-(x^2-7x+6) is 56/3