What is the integral from 1 to 3 of (15/28 x^2-2) ?

The integral from 1 to 3 of (15/28 x^2-2) is 9/14

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integral from 1 to 3 of (15/28 x^2-2)

\int_{1}^{3} (\frac{15}{28} x^{2} - 2) d x

\frac{9}{14}

Decimal

0.64285 \dots

Solution steps

\int_{1}^{3} \frac{15}{28} x^{2} - 2 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_{1}^{3} \frac{15}{28} x^{2} d x - \int_{1}^{3} 2 d x

\int_{1}^{3} \frac{15}{28} x^{2} d x = \frac{65}{14}

\int_{1}^{3} 2 d x = 4

= \frac{65}{14} - 4

Simplify

\frac{65}{14} - 4 : \frac{9}{14}

= \frac{9}{14}

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What is the integral from 1 to 3 of (15/28 x^2-2) ?
The integral from 1 to 3 of (15/28 x^2-2) is 9/14