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

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

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

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

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

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

Expand

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

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

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

\int_{- 2}^{3} 2 x d x = 5

\int_{- 2}^{3} 3 d x = 15

= \frac{35}{3} + 5 - 15

Simplify

\frac{35}{3} + 5 - 15 : \frac{5}{3}

= \frac{5}{3}

\int_{0}^{1} \frac{5}{( 2 x + 1 ) ^{2}} d x

\int_{- 5}^{5} 5 ∣ x ∣ - x^{2} d x

\int_{1}^{5} (6 - x) d x

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

\int_{2}^{5} x^{3} - x^{2} + 8 d x

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