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

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

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

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

\frac{3}{2}

Decimal

1.5

Solution steps

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

Expand

(2 x + 3) (1 - x) : - 2 x^{2} - x + 3

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

\int_{- 1}^{2} 2 x^{2} d x = 6

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

\int_{- 1}^{2} 3 d x = 9

= - 6 - \frac{3}{2} + 9

Simplify

- 6 - \frac{3}{2} + 9 : \frac{3}{2}

= \frac{3}{2}

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