What is the integral from 2 to 5 of 2x^2-x-1 ?

The integral from 2 to 5 of 2x^2-x-1 is 129/2

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integral from 2 to 5 of 2x^2-x-1

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

\frac{129}{2}

Decimal Notation

64.5

Solution steps

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

\int_{2}^{5} 2 x^{2} d x = 78

\int_{2}^{5} x d x = \frac{21}{2}

\int_{2}^{5} 1 d x = 3

= 78 - \frac{21}{2} - 3

Simplify

78 - \frac{21}{2} - 3 : \frac{129}{2}

= \frac{129}{2}

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What is the integral from 2 to 5 of 2x^2-x-1 ?
The integral from 2 to 5 of 2x^2-x-1 is 129/2