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

The integral from-1 to 2 of (x^3-5x^2+3x-1) is -39/4

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

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

- \frac{39}{4}

Decimal Notation

- 9.75

Solution steps

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

\int_{- 1}^{2} x^{3} d x = \frac{15}{4}

\int_{- 1}^{2} 5 x^{2} d x = 15

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

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

= \frac{15}{4} - 15 + \frac{9}{2} - 3

Simplify

\frac{15}{4} - 15 + \frac{9}{2} - 3 : - \frac{39}{4}

= - \frac{39}{4}

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What is the integral from-1 to 2 of (x^3-5x^2+3x-1) ?
The integral from-1 to 2 of (x^3-5x^2+3x-1) is -39/4