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

The integral from-1 to 1 of x^3-2x^2+5 is 26/3

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

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

\frac{26}{3}

Decimal Notation

8.66666 \dots

Solution steps

\int_{- 1}^{1} x^{3} - 2 x^{2} + 5 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 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 d x = 10

= 0 - \frac{4}{3} + 10

Simplify

0 - \frac{4}{3} + 10 : \frac{26}{3}

= \frac{26}{3}

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

\int_{- 3}^{0} ln (y^{2} + 5) d y

\int_{1}^{4} \frac{1}{x ^{3}} + x d x

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

\int_{y^{2}}^{y} (x^{n} + y^{n}) d x

What is the integral from-1 to 1 of x^3-2x^2+5 ?
The integral from-1 to 1 of x^3-2x^2+5 is 26/3