What is the integral from 2 to 4 of (5x^3+2x^2-3x-8) ?

The integral from 2 to 4 of (5x^3+2x^2-3x-8) is 910/3

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integral from 2 to 4 of (5x^3+2x^2-3x-8)

\int_{2}^{4} (5 x^{3} + 2 x^{2} - 3 x - 8) d x

\frac{910}{3}

Decimal

303.33333 \dots

Solution steps

\int_{2}^{4} 5 x^{3} + 2 x^{2} - 3 x - 8 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}^{4} 5 x^{3} d x + \int_{2}^{4} 2 x^{2} d x - \int_{2}^{4} 3 x d x - \int_{2}^{4} 8 d x

\int_{2}^{4} 5 x^{3} d x = 300

\int_{2}^{4} 2 x^{2} d x = \frac{112}{3}

\int_{2}^{4} 3 x d x = 18

\int_{2}^{4} 8 d x = 16

= 300 + \frac{112}{3} - 18 - 16

Simplify

300 + \frac{112}{3} - 18 - 16 : \frac{910}{3}

= \frac{910}{3}

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What is the integral from 2 to 4 of (5x^3+2x^2-3x-8) ?
The integral from 2 to 4 of (5x^3+2x^2-3x-8) is 910/3