What is the integral from-2 to 2 of (4x^3+6x^2-8x+5) ?

The integral from-2 to 2 of (4x^3+6x^2-8x+5) is 52

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integral from-2 to 2 of (4x^3+6x^2-8x+5)

\int_{- 2}^{2} (4 x^{3} + 6 x^{2} - 8 x + 5) d x

52

Solution steps

\int_{- 2}^{2} 4 x^{3} + 6 x^{2} - 8 x + 5 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}^{2} 4 x^{3} d x + \int_{- 2}^{2} 6 x^{2} d x - \int_{- 2}^{2} 8 x d x + \int_{- 2}^{2} 5 d x

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

\int_{- 2}^{2} 6 x^{2} d x = 32

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

\int_{- 2}^{2} 5 d x = 20

= 0 + 32 - 0 + 20

Simplify

= 52

\int 2400 x 3 + 2 x d x

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

\frac{s}{1 + s}

\int \frac{1}{484 + x ^{2}} d x

What is the integral from-2 to 2 of (4x^3+6x^2-8x+5) ?
The integral from-2 to 2 of (4x^3+6x^2-8x+5) is 52