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

The integral from 1 to 3 of (x^2+2x-2) is 38/3

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integral from 1 to 3 of (x^2+2x-2)

\int_{1}^{3} (x^{2} + 2 x - 2) d x

\frac{38}{3}

Decimal

12.66666 \dots

Solution steps

\int_{1}^{3} x^{2} + 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

= \int_{1}^{3} x^{2} d x + \int_{1}^{3} 2 x d x - \int_{1}^{3} 2 d x

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 2 d x = 4

= \frac{26}{3} + 8 - 4

Simplify

\frac{26}{3} + 8 - 4 : \frac{38}{3}

= \frac{38}{3}

What is the integral from 1 to 3 of (x^2+2x-2) ?
The integral from 1 to 3 of (x^2+2x-2) is 38/3