What is the integral from 4 to 2 of (6x^2-2x+1) ?

The integral from 4 to 2 of (6x^2-2x+1) is -102

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integral from 4 to 2 of (6x^2-2x+1)

\int_{4}^{2} (6 x^{2} - 2 x + 1) d x

- 102

Solution steps

\int_{4}^{2} 6 x^{2} - 2 x + 1 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{2}^{4} 6 x^{2} - 2 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_{2}^{4} 6 x^{2} d x - \int_{2}^{4} 2 x d x + \int_{2}^{4} 1 d x)

\int_{2}^{4} 6 x^{2} d x = 112

\int_{2}^{4} 2 x d x = 12

\int_{2}^{4} 1 d x = 2

= - (112 - 12 + 2)

Simplify

= - 102

\frac{\partial}{\partial x} (- 3 y (- 2 x - y - 9))

(2 t - 1)^{2}

3 δ (t) + 2 + 4 e^{- 3 t + 2}

\frac{\partial}{\partial x} (\frac{y}{1 + x ^{2}})

(60 + 2 t)^{\frac{2}{3}}

What is the integral from 4 to 2 of (6x^2-2x+1) ?
The integral from 4 to 2 of (6x^2-2x+1) is -102