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

The integral from-1 to 2 of (x^2-x-3)^2 is 201/10

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

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

\frac{201}{10}

Decimal

20.1

Solution steps

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

Expand

(x^{2} - x - 3)^{2} : x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 9

= \int_{- 1}^{2} x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 9 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}^{2} x^{4} d x - \int_{- 1}^{2} 2 x^{3} d x - \int_{- 1}^{2} 5 x^{2} d x + \int_{- 1}^{2} 6 x d x + \int_{- 1}^{2} 9 d x

\int_{- 1}^{2} x^{4} d x = \frac{33}{5}

\int_{- 1}^{2} 2 x^{3} d x = \frac{15}{2}

\int_{- 1}^{2} 5 x^{2} d x = 15

\int_{- 1}^{2} 6 x d x = 9

\int_{- 1}^{2} 9 d x = 27

= \frac{33}{5} - \frac{15}{2} - 15 + 9 + 27

Simplify

\frac{33}{5} - \frac{15}{2} - 15 + 9 + 27 : \frac{201}{10}

= \frac{201}{10}

What is the integral from-1 to 2 of (x^2-x-3)^2 ?
The integral from-1 to 2 of (x^2-x-3)^2 is 201/10