What is the integral from 3 to 15 of (5x^2-9)/3 ?

The integral from 3 to 15 of (5x^2-9)/3 is 1824

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integral from 3 to 15 of (5x^2-9)/3

\int_{3}^{15} \frac{5 x ^{2} - 9}{3} d x

1824

Solution steps

\int_{3}^{15} \frac{5 x ^{2} - 9}{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}^{15} 5 x^{2} - 9 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}^{15} 5 x^{2} d x - \int_{3}^{15} 9 d x)

\int_{3}^{15} 5 x^{2} d x = 5580

\int_{3}^{15} 9 d x = 108

= \frac{1}{3} (5580 - 108)

Simplify

\frac{1}{3} (5580 - 108) : 1824

= 1824

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What is the integral from 3 to 15 of (5x^2-9)/3 ?
The integral from 3 to 15 of (5x^2-9)/3 is 1824