What is the integral from 2 to 6 of 4x+12-x^2 ?

The integral from 2 to 6 of 4x+12-x^2 is 128/3

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integral from 2 to 6 of 4x+12-x^2

\int_{2}^{6} 4 x + 12 - x^{2} d x

\frac{128}{3}

Decimal

42.66666 \dots

Solution steps

\int_{2}^{6} 4 x + 12 - 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

= \int_{2}^{6} 4 x d x + \int_{2}^{6} 12 d x - \int_{2}^{6} x^{2} d x

\int_{2}^{6} 4 x d x = 64

\int_{2}^{6} 12 d x = 48

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

= 64 + 48 - \frac{208}{3}

Simplify

64 + 48 - \frac{208}{3} : \frac{128}{3}

= \frac{128}{3}

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What is the integral from 2 to 6 of 4x+12-x^2 ?
The integral from 2 to 6 of 4x+12-x^2 is 128/3