What is the integral from-2 to 0 of 12x^3-14x^2 ?

The integral from-2 to 0 of 12x^3-14x^2 is -256/3

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integral from-2 to 0 of 12x^3-14x^2

\int_{- 2}^{0} 12 x^{3} - 14 x^{2} d x

- \frac{256}{3}

Decimal

- 85.33333 \dots

Solution steps

\int_{- 2}^{0} 12 x^{3} - 14 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_{- 2}^{0} 12 x^{3} d x - \int_{- 2}^{0} 14 x^{2} d x

\int_{- 2}^{0} 12 x^{3} d x = - 48

\int_{- 2}^{0} 14 x^{2} d x = \frac{112}{3}

= - 48 - \frac{112}{3}

Simplify

- 48 - \frac{112}{3} : - \frac{256}{3}

= - \frac{256}{3}

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

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

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

\int_{0}^{1} \frac{x}{1 + 6 x ^{2}} d x

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

What is the integral from-2 to 0 of 12x^3-14x^2 ?
The integral from-2 to 0 of 12x^3-14x^2 is -256/3