What is the integral from-1 to 1 of (x^3-2x^2-5x+6) ?

The integral from-1 to 1 of (x^3-2x^2-5x+6) is 32/3

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integral from-1 to 1 of (x^3-2x^2-5x+6)

\int_{- 1}^{1} (x^{3} - 2 x^{2} - 5 x + 6) d x

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

\int_{- 1}^{1} x^{3} - 2 x^{2} - 5 x + 6 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}^{1} x^{3} d x - \int_{- 1}^{1} 2 x^{2} d x - \int_{- 1}^{1} 5 x d x + \int_{- 1}^{1} 6 d x

\int_{- 1}^{1} x^{3} d x = 0

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

\int_{- 1}^{1} 5 x d x = 0

\int_{- 1}^{1} 6 d x = 12

= 0 - \frac{4}{3} - 0 + 12

Simplify

0 - \frac{4}{3} - 0 + 12 : \frac{32}{3}

= \frac{32}{3}

\int_{0}^{c o s (x)} 3^{x^{2}} d x

\int_{0}^{4} \frac{x ^{2} - 8 x + 16}{16} d x

\int_{0}^{2} 0.5 x^{2} d x

\int_{0}^{1} x \frac{2 ( x + 1 )}{3} d x

What is the integral from-1 to 1 of (x^3-2x^2-5x+6) ?
The integral from-1 to 1 of (x^3-2x^2-5x+6) is 32/3