What is the integral from 1 to 4 of (5-2x+3x^2) ?

The integral from 1 to 4 of (5-2x+3x^2) is 63

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integral from 1 to 4 of (5-2x+3x^2)

\int_{1}^{4} (5 - 2 x + 3 x^{2}) d x

63

Solution steps

\int_{1}^{4} 5 - 2 x + 3 x^{2} 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} 5 d x - \int_{1}^{4} 2 x d x + \int_{1}^{4} 3 x^{2} d x

\int_{1}^{4} 5 d x = 15

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} 3 x^{2} d x = 63

= 15 - 15 + 63

Simplify

= 63

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What is the integral from 1 to 4 of (5-2x+3x^2) ?
The integral from 1 to 4 of (5-2x+3x^2) is 63