What is the integral from 0 to 6 of 2x^2-16x+30 ?

The integral from 0 to 6 of 2x^2-16x+30 is 36

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integral from 0 to 6 of 2x^2-16x+30

\int_{0}^{6} 2 x^{2} - 16 x + 30 d x

36

Solution steps

\int_{0}^{6} 2 x^{2} - 16 x + 30 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_{0}^{6} 2 x^{2} d x - \int_{0}^{6} 16 x d x + \int_{0}^{6} 30 d x

\int_{0}^{6} 2 x^{2} d x = 144

\int_{0}^{6} 16 x d x = 288

\int_{0}^{6} 30 d x = 180

= 144 - 288 + 180

Simplify

= 36

\frac{d}{d x} (- 4 e^{- 2 x^{2}} x)

f (x) = 13 x^{- 3}

x \to 0 lim ((1 + 3 x)^{\frac{5}{x}})

\int 5 x e^{6 x} d x

(e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x} - \frac{5 e ^{\frac{1}{x}}}{x ^{2}})^{^{'}}

What is the integral from 0 to 6 of 2x^2-16x+30 ?
The integral from 0 to 6 of 2x^2-16x+30 is 36