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

The integral from 2 to 6 of (3+4x^2) is 868/3

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integral from 2 to 6 of (3+4x^2)

\int_{2}^{6} (3 + 4 x^{2}) d x

\frac{868}{3}

Decimal

289.33333 \dots

Solution steps

\int_{2}^{6} 3 + 4 x^{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}^{6} 3 d x + \int_{2}^{6} 4 x^{2} d x

\int_{2}^{6} 3 d x = 12

\int_{2}^{6} 4 x^{2} d x = \frac{832}{3}

= 12 + \frac{832}{3}

Simplify

12 + \frac{832}{3} : \frac{868}{3}

= \frac{868}{3}

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What is the integral from 2 to 6 of (3+4x^2) ?
The integral from 2 to 6 of (3+4x^2) is 868/3