What is the integral from-1 to 3 of (3x-5)(x+2) ?

The integral from-1 to 3 of (3x-5)(x+2) is -8

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integral from-1 to 3 of (3x-5)(x+2)

\int_{- 1}^{3} (3 x - 5) (x + 2) d x

- 8

Solution steps

\int_{- 1}^{3} (3 x - 5) (x + 2) d x

Expand

(3 x - 5) (x + 2) : 3 x^{2} + x - 10

= \int_{- 1}^{3} 3 x^{2} + x - 10 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_{- 1}^{3} 3 x^{2} d x + \int_{- 1}^{3} x d x - \int_{- 1}^{3} 10 d x

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} x d x = 4

\int_{- 1}^{3} 10 d x = 40

= 28 + 4 - 40

Simplify

= - 8

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\int_{0}^{0.1} 600 x d x

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What is the integral from-1 to 3 of (3x-5)(x+2) ?
The integral from-1 to 3 of (3x-5)(x+2) is -8