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

The integral from-2 to 3 of (3x-2)(x+3) is 45/2

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

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

\frac{45}{2}

Decimal

22.5

Solution steps

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

Multiply by the conjugate of

3 x - 2 : \frac{9 x ^{2} - 4}{3 x + 2}

= \int_{- 2}^{3} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x

Find undefined (singularity) points:

x = - \frac{2}{3}

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 2}^{- \frac{2}{3}} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x + \int_{- \frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x

\int_{- 2}^{- \frac{2}{3}} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x = - \frac{344}{27}

\int_{- \frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x + 2} (x + 3) d x = \frac{1903}{54}

= - \frac{344}{27} + \frac{1903}{54}

Simplify

- \frac{344}{27} + \frac{1903}{54} : \frac{45}{2}

= \frac{45}{2}

What is the integral from-2 to 3 of (3x-2)(x+3) ?
The integral from-2 to 3 of (3x-2)(x+3) is 45/2