What is the integral from 7 to 0 of |2x-7| ?

The integral from 7 to 0 of |2x-7| is -49/2

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integral from 7 to 0 of |2x-7|

\int_{7}^{0} ∣ 2 x - 7 ∣ d x

- \frac{49}{2}

Decimal Notation

- 24.5

Solution steps

\int_{7}^{0} ∣ 2 x - 7 ∣ d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{7} ∣ 2 x - 7 ∣ d x

Eliminate Absolutes

= - (\int_{0}^{\frac{7}{2}} - 2 x + 7 d x + \int_{\frac{7}{2}}^{7} 2 x - 7 d x)

\int_{0}^{\frac{7}{2}} - 2 x + 7 d x = \frac{49}{4}

\int_{\frac{7}{2}}^{7} 2 x - 7 d x = \frac{49}{4}

= - (\frac{49}{4} + \frac{49}{4})

Simplify

- (\frac{49}{4} + \frac{49}{4}) : - \frac{49}{2}

= - \frac{49}{2}

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What is the integral from 7 to 0 of |2x-7| ?
The integral from 7 to 0 of |2x-7| is -49/2