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

The integral from 1 to 4 of (x^2-2x+5) is 21

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

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

21

Solution steps

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

\int_{1}^{4} x^{2} d x = 21

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

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

= 21 - 15 + 15

Simplify

= 21

What is the integral from 1 to 4 of (x^2-2x+5) ?
The integral from 1 to 4 of (x^2-2x+5) is 21