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

The integral from-1 to 2 of (x^3-x^2+2) is 27/4

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

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

\frac{27}{4}

Decimal

6.75

Solution steps

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

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

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

\int_{- 1}^{2} 2 d x = 6

= \frac{15}{4} - 3 + 6

Simplify

\frac{15}{4} - 3 + 6 : \frac{27}{4}

= \frac{27}{4}

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What is the integral from-1 to 2 of (x^3-x^2+2) ?
The integral from-1 to 2 of (x^3-x^2+2) is 27/4