What is the integral from-2 to 3 of (5x^2-3x-2)^2 ?

The integral from-2 to 3 of (5x^2-3x-2)^2 is 4855/6

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integral from-2 to 3 of (5x^2-3x-2)^2

\int_{- 2}^{3} (5 x^{2} - 3 x - 2)^{2} d x

\frac{4855}{6}

Decimal

809.16666 \dots

Solution steps

\int_{- 2}^{3} (5 x^{2} - 3 x - 2)^{2} d x

Expand

(5 x^{2} - 3 x - 2)^{2} : 25 x^{4} - 30 x^{3} - 11 x^{2} + 12 x + 4

= \int_{- 2}^{3} 25 x^{4} - 30 x^{3} - 11 x^{2} + 12 x + 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

= \int_{- 2}^{3} 25 x^{4} d x - \int_{- 2}^{3} 30 x^{3} d x - \int_{- 2}^{3} 11 x^{2} d x + \int_{- 2}^{3} 12 x d x + \int_{- 2}^{3} 4 d x

\int_{- 2}^{3} 25 x^{4} d x = 1375

\int_{- 2}^{3} 30 x^{3} d x = \frac{975}{2}

\int_{- 2}^{3} 11 x^{2} d x = \frac{385}{3}

\int_{- 2}^{3} 12 x d x = 30

\int_{- 2}^{3} 4 d x = 20

= 1375 - \frac{975}{2} - \frac{385}{3} + 30 + 20

Simplify

1375 - \frac{975}{2} - \frac{385}{3} + 30 + 20 : \frac{4855}{6}

= \frac{4855}{6}

What is the integral from-2 to 3 of (5x^2-3x-2)^2 ?
The integral from-2 to 3 of (5x^2-3x-2)^2 is 4855/6