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

The integral from-1 to 4 of (x^2+x-2) is 115/6

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

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

\frac{115}{6}

Decimal

19.16666 \dots

Solution steps

\int_{- 1}^{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

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

\int_{- 1}^{4} x^{2} d x = \frac{65}{3}

\int_{- 1}^{4} x d x = \frac{15}{2}

\int_{- 1}^{4} 2 d x = 10

= \frac{65}{3} + \frac{15}{2} - 10

Simplify

\frac{65}{3} + \frac{15}{2} - 10 : \frac{115}{6}

= \frac{115}{6}

What is the integral from-1 to 4 of (x^2+x-2) ?
The integral from-1 to 4 of (x^2+x-2) is 115/6