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

The integral from 1 to 2 of 2(x^2-4) is -10/3

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

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

- \frac{10}{3}

Decimal Notation

- 3.33333 \dots

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{1}^{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

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

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

= 2 (\frac{7}{3} - 4)

Simplify

2 (\frac{7}{3} - 4) : - \frac{10}{3}

= - \frac{10}{3}

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What is the integral from 1 to 2 of 2(x^2-4) ?
The integral from 1 to 2 of 2(x^2-4) is -10/3