What is the integral from-2 to 2 of 2x^2-6x+14 ?

The integral from-2 to 2 of 2x^2-6x+14 is 200/3

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integral from-2 to 2 of 2x^2-6x+14

\int_{- 2}^{2} 2 x^{2} - 6 x + 14 d x

\frac{200}{3}

Decimal

66.66666 \dots

Solution steps

\int_{- 2}^{2} 2 x^{2} - 6 x + 14 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} 2 x^{2} d x - \int_{- 2}^{2} 6 x d x + \int_{- 2}^{2} 14 d x

\int_{- 2}^{2} 2 x^{2} d x = \frac{32}{3}

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

\int_{- 2}^{2} 14 d x = 56

= \frac{32}{3} - 0 + 56

Simplify

\frac{32}{3} - 0 + 56 : \frac{200}{3}

= \frac{200}{3}

\int x^{2} - 2 x + 8 d x

\frac{d}{d x} (\frac{2 x ^{2} + 6 x + 4}{x})

x \to \infty lim (\frac{n !}{n})

\int \frac{x + 1}{x ^{2} + 4 x + 3} d x

\int_{6}^{8} \frac{30}{( x - 6 ) ^{3}} d x

What is the integral from-2 to 2 of 2x^2-6x+14 ?
The integral from-2 to 2 of 2x^2-6x+14 is 200/3