What is the integral from 2 to 7 of (4x^2-2x) ?

The integral from 2 to 7 of (4x^2-2x) is 1205/3

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integral from 2 to 7 of (4x^2-2x)

\int_{2}^{7} (4 x^{2} - 2 x) d x

\frac{1205}{3}

Decimal

401.66666 \dots

Solution steps

\int_{2}^{7} 4 x^{2} - 2 x 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}^{7} 4 x^{2} d x - \int_{2}^{7} 2 x d x

\int_{2}^{7} 4 x^{2} d x = \frac{1340}{3}

\int_{2}^{7} 2 x d x = 45

= \frac{1340}{3} - 45

Simplify

\frac{1340}{3} - 45 : \frac{1205}{3}

= \frac{1205}{3}

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What is the integral from 2 to 7 of (4x^2-2x) ?
The integral from 2 to 7 of (4x^2-2x) is 1205/3