What is the integral from 3 to 10 of (5x^2-8)/3 ?

The integral from 3 to 10 of (5x^2-8)/3 is 4697/9

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integral from 3 to 10 of (5x^2-8)/3

\int_{3}^{10} \frac{5 x ^{2} - 8}{3} d x

\frac{4697}{9}

Decimal

521.88888 \dots

Solution steps

\int_{3}^{10} \frac{5 x ^{2} - 8}{3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{3}^{10} 5 x^{2} - 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

= \frac{1}{3} (\int_{3}^{10} 5 x^{2} d x - \int_{3}^{10} 8 d x)

\int_{3}^{10} 5 x^{2} d x = \frac{4865}{3}

\int_{3}^{10} 8 d x = 56

= \frac{1}{3} (\frac{4865}{3} - 56)

Simplify

\frac{1}{3} (\frac{4865}{3} - 56) : \frac{4697}{9}

= \frac{4697}{9}

What is the integral from 3 to 10 of (5x^2-8)/3 ?
The integral from 3 to 10 of (5x^2-8)/3 is 4697/9