What is the integral from 0 to 7 of |x^2-6x+5| ?

The integral from 0 to 7 of |x^2-6x+5| is 71/3

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integral from 0 to 7 of |x^2-6x+5|

\int_{0}^{7} x^{2} - 6 x + 5 d x

\frac{71}{3}

Decimal

23.66666 \dots

Solution steps

\int_{0}^{7} x^{2} - 6 x + 5 d x

Eliminate Absolutes

= \int_{0}^{1} x^{2} - 6 x + 5 d x + \int_{1}^{5} - x^{2} + 6 x - 5 d x + \int_{5}^{7} x^{2} - 6 x + 5 d x

\int_{0}^{1} x^{2} - 6 x + 5 d x = \frac{7}{3}

\int_{1}^{5} - x^{2} + 6 x - 5 d x = \frac{32}{3}

\int_{5}^{7} x^{2} - 6 x + 5 d x = \frac{32}{3}

= \frac{7}{3} + \frac{32}{3} + \frac{32}{3}

Simplify

\frac{7}{3} + \frac{32}{3} + \frac{32}{3} : \frac{71}{3}

= \frac{71}{3}

\int 2 e^{2 x} sin (2 x) d x

\frac{d}{d x} ((2 x^{2} + 3)^{2})

\frac{2}{s + 1} + 8 a \cdot \frac{s}{s ^{2} + 9}

\frac{d}{d x} ((1 - 2 x)^{5} (3 x - 2)^{6})

2 e^{2 t} + 8 t e^{2 t} + 4 t^{2} e^{2 t}

What is the integral from 0 to 7 of |x^2-6x+5| ?
The integral from 0 to 7 of |x^2-6x+5| is 71/3