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

The integral from 3 to 6 of (3x^2+x-3) is 387/2

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

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

\frac{387}{2}

Decimal

193.5

Solution steps

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

\int_{3}^{6} 3 x^{2} d x = 189

\int_{3}^{6} x d x = \frac{27}{2}

\int_{3}^{6} 3 d x = 9

= 189 + \frac{27}{2} - 9

Simplify

189 + \frac{27}{2} - 9 : \frac{387}{2}

= \frac{387}{2}

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What is the integral from 3 to 6 of (3x^2+x-3) ?
The integral from 3 to 6 of (3x^2+x-3) is 387/2