What is the integral from 0 to 3 of (3x+2)(x-5) ?

The integral from 0 to 3 of (3x+2)(x-5) is -123/2

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integral from 0 to 3 of (3x+2)(x-5)

\int_{0}^{3} (3 x + 2) (x - 5) d x

- \frac{123}{2}

Decimal

- 61.5

Solution steps

\int_{0}^{3} (3 x + 2) (x - 5) d x

Multiply by the conjugate of

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

= \int_{0}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) 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_{0}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x + \int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x

\int_{0}^{\frac{2}{3}} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x = - \frac{250}{27}

\int_{\frac{2}{3}}^{3} \frac{9 x ^{2} - 4}{3 x - 2} (x - 5) d x = - \frac{2821}{54}

= - \frac{250}{27} - \frac{2821}{54}

Simplify

- \frac{250}{27} - \frac{2821}{54} : - \frac{123}{2}

= - \frac{123}{2}

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What is the integral from 0 to 3 of (3x+2)(x-5) ?
The integral from 0 to 3 of (3x+2)(x-5) is -123/2