What is the integral from 1 to 5 of |x^2-6x+8| ?

The integral from 1 to 5 of |x^2-6x+8| is 4

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integral from 1 to 5 of |x^2-6x+8|

\int_{1}^{5} x^{2} - 6 x + 8 d x

4

Solution steps

\int_{1}^{5} x^{2} - 6 x + 8 d x

Eliminate Absolutes

= \int_{1}^{2} x^{2} - 6 x + 8 d x + \int_{2}^{4} - x^{2} + 6 x - 8 d x + \int_{4}^{5} x^{2} - 6 x + 8 d x

\int_{1}^{2} x^{2} - 6 x + 8 d x = \frac{4}{3}

\int_{2}^{4} - x^{2} + 6 x - 8 d x = \frac{4}{3}

\int_{4}^{5} x^{2} - 6 x + 8 d x = \frac{4}{3}

= \frac{4}{3} + \frac{4}{3} + \frac{4}{3}

Simplify

\frac{4}{3} + \frac{4}{3} + \frac{4}{3} : 4

= 4

\int 7 x^{4} - 5 x^{3} + 5 x^{2} + C d x

\frac{7}{x}, x = 1, x = 41

x \to - 7 - lim (x^{2} + 7)

\frac{d y}{d x} = 2 + 2 y + x + x y

f (x) = c x^{- 2}

What is the integral from 1 to 5 of |x^2-6x+8| ?
The integral from 1 to 5 of |x^2-6x+8| is 4