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

The integral from-1 to 3 of (x^2-2x-3) is -32/3

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

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

- \frac{32}{3}

Decimal Notation

- 10.66666 \dots

Solution steps

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

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

\int_{- 1}^{3} 2 x d x = 8

\int_{- 1}^{3} 3 d x = 12

= \frac{28}{3} - 8 - 12

Simplify

\frac{28}{3} - 8 - 12 : - \frac{32}{3}

= - \frac{32}{3}

\frac{( 2 x + 1 )}{x + 2}

\int \frac{x - 1}{x ^{2} - x - 2} d x

\frac{d}{d t} (2 t^{4})

sin (x^{2} + x)

\frac{d}{d x} (\frac{1}{1 + e ^{- w x}})

What is the integral from-1 to 3 of (x^2-2x-3) ?
The integral from-1 to 3 of (x^2-2x-3) is -32/3