What is the integral from-1 to 0 of (x^3-2x+3) ?

The integral from-1 to 0 of (x^3-2x+3) is 15/4

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integral from-1 to 0 of (x^3-2x+3)

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

\frac{15}{4}

Decimal

3.75

Solution steps

\int_{- 1}^{0} x^{3} - 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}^{0} x^{3} d x - \int_{- 1}^{0} 2 x d x + \int_{- 1}^{0} 3 d x

\int_{- 1}^{0} x^{3} d x = - \frac{1}{4}

\int_{- 1}^{0} 2 x d x = - 1

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

= - \frac{1}{4} - (- 1) + 3

Simplify

- \frac{1}{4} - (- 1) + 3 : \frac{15}{4}

= \frac{15}{4}

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What is the integral from-1 to 0 of (x^3-2x+3) ?
The integral from-1 to 0 of (x^3-2x+3) is 15/4