What is the integral from 2 to 6 of (2x^2+4) ?

The integral from 2 to 6 of (2x^2+4) is 464/3

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integral from 2 to 6 of (2x^2+4)

\int_{2}^{6} (2 x^{2} + 4) d x

\frac{464}{3}

Decimal

154.66666 \dots

Solution steps

\int_{2}^{6} 2 x^{2} + 4 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}^{6} 2 x^{2} d x + \int_{2}^{6} 4 d x

\int_{2}^{6} 2 x^{2} d x = \frac{416}{3}

\int_{2}^{6} 4 d x = 16

= \frac{416}{3} + 16

Simplify

\frac{416}{3} + 16 : \frac{464}{3}

= \frac{464}{3}

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What is the integral from 2 to 6 of (2x^2+4) ?
The integral from 2 to 6 of (2x^2+4) is 464/3