What is the integral from 0 to 4 of 5x^2-2x+10 ?

The integral from 0 to 4 of 5x^2-2x+10 is 392/3

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integral from 0 to 4 of 5x^2-2x+10

\int_{0}^{4} 5 x^{2} - 2 x + 10 d x

\frac{392}{3}

Decimal

130.66666 \dots

Solution steps

\int_{0}^{4} 5 x^{2} - 2 x + 10 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_{0}^{4} 5 x^{2} d x - \int_{0}^{4} 2 x d x + \int_{0}^{4} 10 d x

\int_{0}^{4} 5 x^{2} d x = \frac{320}{3}

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 10 d x = 40

= \frac{320}{3} - 16 + 40

Simplify

\frac{320}{3} - 16 + 40 : \frac{392}{3}

= \frac{392}{3}

What is the integral from 0 to 4 of 5x^2-2x+10 ?
The integral from 0 to 4 of 5x^2-2x+10 is 392/3