What is the integral from-1 to 2 of (3x-8)(x+3) ?

The integral from-1 to 2 of (3x-8)(x+3) is -123/2

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integral from-1 to 2 of (3x-8)(x+3)

\int_{- 1}^{2} (3 x - 8) (x + 3) d x

- \frac{123}{2}

Decimal

- 61.5

Solution steps

\int_{- 1}^{2} (3 x - 8) (x + 3) d x

Apply Integration By Parts

: [(3 x - 8) (\frac{x ^{2}}{2} + 3 x) - \int 3 (\frac{x ^{2}}{2} + 3 x) d x]_{- 1}^{2}

= [(3 x - 8) (\frac{x ^{2}}{2} + 3 x) - \int 3 (\frac{x ^{2}}{2} + 3 x) d x]_{- 1}^{2}

\int 3 (\frac{x ^{2}}{2} + 3 x) d x = 3 (\frac{x ^{3}}{6} + \frac{3 x ^{2}}{2})

= [(3 x - 8) (\frac{x ^{2}}{2} + 3 x) - 3 (\frac{x ^{3}}{6} + \frac{3 x ^{2}}{2})]_{- 1}^{2}

Compute the boundaries:

- \frac{123}{2}

= - \frac{123}{2}

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What is the integral from-1 to 2 of (3x-8)(x+3) ?
The integral from-1 to 2 of (3x-8)(x+3) is -123/2