What is the integral from-2 to 0 of 2x^3+6x^2+4x ?

The integral from-2 to 0 of 2x^3+6x^2+4x is 0

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integral from-2 to 0 of 2x^3+6x^2+4x

\int_{- 2}^{0} 2 x^{3} + 6 x^{2} + 4 x d x

0

Solution steps

\int_{- 2}^{0} 2 x^{3} + 6 x^{2} + 4 x 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} 2 x^{3} d x + \int_{- 2}^{0} 6 x^{2} d x + \int_{- 2}^{0} 4 x d x

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

\int_{- 2}^{0} 6 x^{2} d x = 16

\int_{- 2}^{0} 4 x d x = - 8

= - 8 + 16 - 8

Simplify

= 0

\int_{0}^{8} (x - \frac{1}{2}) d x

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\int_{\frac{π}{3}}^{\frac{π}{2}} x + cos (x) d x

What is the integral from-2 to 0 of 2x^3+6x^2+4x ?
The integral from-2 to 0 of 2x^3+6x^2+4x is 0