What is the integral from 1 to 2 of 3/8 (4x-2x^2) ?

The integral from 1 to 2 of 3/8 (4x-2x^2) is 1/2

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integral from 1 to 2 of 3/8 (4x-2x^2)

\int_{1}^{2} \frac{3}{8} (4 x - 2 x^{2}) d x

\frac{1}{2}

Decimal

0.5

Solution steps

\int_{1}^{2} \frac{3}{8} (4 x - 2 x^{2}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{3}{8} \cdot \int_{1}^{2} 4 x - 2 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

= \frac{3}{8} (\int_{1}^{2} 4 x d x - \int_{1}^{2} 2 x^{2} d x)

\int_{1}^{2} 4 x d x = 6

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

= \frac{3}{8} (6 - \frac{14}{3})

Simplify

\frac{3}{8} (6 - \frac{14}{3}) : \frac{1}{2}

= \frac{1}{2}

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What is the integral from 1 to 2 of 3/8 (4x-2x^2) ?
The integral from 1 to 2 of 3/8 (4x-2x^2) is 1/2