What is the integral from 1 to 4 of (8x^2-6x+4) ?

The integral from 1 to 4 of (8x^2-6x+4) is 135

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integral from 1 to 4 of (8x^2-6x+4)

\int_{1}^{4} (8 x^{2} - 6 x + 4) d x

135

Solution steps

\int_{1}^{4} 8 x^{2} - 6 x + 4 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_{1}^{4} 8 x^{2} d x - \int_{1}^{4} 6 x d x + \int_{1}^{4} 4 d x

\int_{1}^{4} 8 x^{2} d x = 168

\int_{1}^{4} 6 x d x = 45

\int_{1}^{4} 4 d x = 12

= 168 - 45 + 12

Simplify

= 135

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What is the integral from 1 to 4 of (8x^2-6x+4) ?
The integral from 1 to 4 of (8x^2-6x+4) is 135