What is the integral from-2 to 5 of (10x-x^2) ?

The integral from-2 to 5 of (10x-x^2) is 182/3

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integral from-2 to 5 of (10x-x^2)

\int_{- 2}^{5} (10 x - x^{2}) d x

\frac{182}{3}

Decimal Notation

60.66666 \dots

Solution steps

\int_{- 2}^{5} 10 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

= \int_{- 2}^{5} 10 x d x - \int_{- 2}^{5} x^{2} d x

\int_{- 2}^{5} 10 x d x = 105

\int_{- 2}^{5} x^{2} d x = \frac{133}{3}

= 105 - \frac{133}{3}

Simplify

105 - \frac{133}{3} : \frac{182}{3}

= \frac{182}{3}

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What is the integral from-2 to 5 of (10x-x^2) ?
The integral from-2 to 5 of (10x-x^2) is 182/3