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

The integral from-2 to 0 of (x^4-2x^3+3) is 102/5

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integral from-2 to 0 of (x^4-2x^3+3)

\int_{- 2}^{0} (x^{4} - 2 x^{3} + 3) d x

\frac{102}{5}

Decimal

20.4

Solution steps

\int_{- 2}^{0} x^{4} - 2 x^{3} + 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_{- 2}^{0} x^{4} d x - \int_{- 2}^{0} 2 x^{3} d x + \int_{- 2}^{0} 3 d x

\int_{- 2}^{0} x^{4} d x = \frac{32}{5}

\int_{- 2}^{0} 2 x^{3} d x = - 8

\int_{- 2}^{0} 3 d x = 6

= \frac{32}{5} - (- 8) + 6

Simplify

\frac{32}{5} - (- 8) + 6 : \frac{102}{5}

= \frac{102}{5}

What is the integral from-2 to 0 of (x^4-2x^3+3) ?
The integral from-2 to 0 of (x^4-2x^3+3) is 102/5