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

The integral from-3 to 3 of (x^3+3x^2+2x) is 54

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

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

54

Solution steps

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

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

\int_{- 3}^{3} 3 x^{2} d x = 54

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

= 0 + 54 + 0

Simplify

= 54

\int_{1}^{3} 2 x^{2} + 4 d x

\int_{0}^{\frac{π}{2}} x sin (y) d y

\int_{- 1}^{0} 2 y + 2 d y

\int_{1}^{25} \frac{3}{x} d x

\int_{1}^{2} \frac{4 x}{1 + x ^{2}} d x

What is the integral from-3 to 3 of (x^3+3x^2+2x) ?
The integral from-3 to 3 of (x^3+3x^2+2x) is 54