What is the integral from-3 to 3 of (5x^3+2x^2+6x-1) ?

The integral from-3 to 3 of (5x^3+2x^2+6x-1) is 30

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integral from-3 to 3 of (5x^3+2x^2+6x-1)

\int_{- 3}^{3} (5 x^{3} + 2 x^{2} + 6 x - 1) d x

30

Solution steps

\int_{- 3}^{3} 5 x^{3} + 2 x^{2} + 6 x - 1 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} 5 x^{3} d x + \int_{- 3}^{3} 2 x^{2} d x + \int_{- 3}^{3} 6 x d x - \int_{- 3}^{3} 1 d x

\int_{- 3}^{3} 5 x^{3} d x = 0

\int_{- 3}^{3} 2 x^{2} d x = 36

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

\int_{- 3}^{3} 1 d x = 6

= 0 + 36 + 0 - 6

Simplify

= 30

\int_{0}^{\frac{π}{2}} cos (x) cos (n x) d x

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

\int_{- π}^{\frac{π}{2}} cos (n x) d x

\int_{0}^{0.5} x cos (π x) d x

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

What is the integral from-3 to 3 of (5x^3+2x^2+6x-1) ?
The integral from-3 to 3 of (5x^3+2x^2+6x-1) is 30