What is the integral from 0 to 10 of |x^2-8x+7| ?

The integral from 0 to 10 of |x^2-8x+7| is 226/3

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integral from 0 to 10 of |x^2-8x+7|

\int_{0}^{10} x^{2} - 8 x + 7 d x

\frac{226}{3}

Decimal

75.33333 \dots

Solution steps

\int_{0}^{10} x^{2} - 8 x + 7 d x

Eliminate Absolutes

= \int_{0}^{1} x^{2} - 8 x + 7 d x + \int_{1}^{7} - x^{2} + 8 x - 7 d x + \int_{7}^{10} x^{2} - 8 x + 7 d x

\int_{0}^{1} x^{2} - 8 x + 7 d x = \frac{10}{3}

\int_{1}^{7} - x^{2} + 8 x - 7 d x = 36

\int_{7}^{10} x^{2} - 8 x + 7 d x = 36

= \frac{10}{3} + 36 + 36

Simplify

\frac{10}{3} + 36 + 36 : \frac{226}{3}

= \frac{226}{3}

\frac{\partial}{\partial y} (7 x + 5 y)

\int \frac{1}{x + 3 x} d x

\frac{\partial}{\partial x} (4 x cos (5 x y))

t^{3} \cdot e^{- 3 t}

\int 5 e^{- 3 x} d x

What is the integral from 0 to 10 of |x^2-8x+7| ?
The integral from 0 to 10 of |x^2-8x+7| is 226/3