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

The integral from 2 to 10 of (5x^2-2) is 4912/3

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

\int_{2}^{10} (5 x^{2} - 2) d x

\frac{4912}{3}

Decimal

1637.33333 \dots

Solution steps

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

\int_{2}^{10} 5 x^{2} d x = \frac{4960}{3}

\int_{2}^{10} 2 d x = 16

= \frac{4960}{3} - 16

Simplify

\frac{4960}{3} - 16 : \frac{4912}{3}

= \frac{4912}{3}

What is the integral from 2 to 10 of (5x^2-2) ?
The integral from 2 to 10 of (5x^2-2) is 4912/3