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

The integral from-2 to 3 of (2x-3)(x-3) is 275/6

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

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

\frac{275}{6}

Decimal

45.83333 \dots

Solution steps

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

Expand

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

= \int_{- 2}^{3} 2 x^{2} - 9 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_{- 2}^{3} 2 x^{2} d x - \int_{- 2}^{3} 9 x d x + \int_{- 2}^{3} 9 d x

\int_{- 2}^{3} 2 x^{2} d x = \frac{70}{3}

\int_{- 2}^{3} 9 x d x = \frac{45}{2}

\int_{- 2}^{3} 9 d x = 45

= \frac{70}{3} - \frac{45}{2} + 45

Simplify

\frac{70}{3} - \frac{45}{2} + 45 : \frac{275}{6}

= \frac{275}{6}

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What is the integral from-2 to 3 of (2x-3)(x-3) ?
The integral from-2 to 3 of (2x-3)(x-3) is 275/6