What is the integral from 3 to 6 of (2x^2+5x-6) ?

The integral from 3 to 6 of (2x^2+5x-6) is 351/2

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integral from 3 to 6 of (2x^2+5x-6)

\int_{3}^{6} (2 x^{2} + 5 x - 6) d x

\frac{351}{2}

Decimal

175.5

Solution steps

\int_{3}^{6} 2 x^{2} + 5 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_{3}^{6} 2 x^{2} d x + \int_{3}^{6} 5 x d x - \int_{3}^{6} 6 d x

\int_{3}^{6} 2 x^{2} d x = 126

\int_{3}^{6} 5 x d x = \frac{135}{2}

\int_{3}^{6} 6 d x = 18

= 126 + \frac{135}{2} - 18

Simplify

126 + \frac{135}{2} - 18 : \frac{351}{2}

= \frac{351}{2}

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What is the integral from 3 to 6 of (2x^2+5x-6) ?
The integral from 3 to 6 of (2x^2+5x-6) is 351/2