What is the integral from-4 to 3 of-x^3+27x+140-6x^2 ?

The integral from-4 to 3 of-x^3+27x+140-6x^2 is 2989/4

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integral from-4 to 3 of-x^3+27x+140-6x^2

\int_{- 4}^{3} - x^{3} + 27 x + 140 - 6 x^{2} d x

\frac{2989}{4}

Decimal

747.25

Solution steps

\int_{- 4}^{3} - x^{3} + 27 x + 140 - 6 x^{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_{- 4}^{3} x^{3} d x + \int_{- 4}^{3} 27 x d x + \int_{- 4}^{3} 140 d x - \int_{- 4}^{3} 6 x^{2} d x

\int_{- 4}^{3} x^{3} d x = - \frac{175}{4}

\int_{- 4}^{3} 27 x d x = - \frac{189}{2}

\int_{- 4}^{3} 140 d x = 980

\int_{- 4}^{3} 6 x^{2} d x = 182

= - (- \frac{175}{4}) - \frac{189}{2} + 980 - 182

Simplify

- (- \frac{175}{4}) - \frac{189}{2} + 980 - 182 : \frac{2989}{4}

= \frac{2989}{4}

What is the integral from-4 to 3 of-x^3+27x+140-6x^2 ?
The integral from-4 to 3 of-x^3+27x+140-6x^2 is 2989/4