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Popular >

integral from 9 to 0 of |2x-9|

Solution

\int_{9}^{0} ∣ 2 x - 9 ∣ d x

Solution

- \frac{81}{2}

+1

Decimal Notation

- 40.5

Solution steps

\int_{9}^{0} ∣ 2 x - 9 ∣ d x

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

= - \int_{0}^{9} ∣ 2 x - 9 ∣ d x

Eliminate Absolutes

= - (\int_{0}^{\frac{9}{2}} - 2 x + 9 d x + \int_{\frac{9}{2}}^{9} 2 x - 9 d x)

\int_{0}^{\frac{9}{2}} - 2 x + 9 d x = \frac{81}{4}

\int_{\frac{9}{2}}^{9} 2 x - 9 d x = \frac{81}{4}

= - (\frac{81}{4} + \frac{81}{4})

Simplify

- (\frac{81}{4} + \frac{81}{4}) : - \frac{81}{2}

= - \frac{81}{2}

Popular Examples

integral from 2 to 10 of 3/(sqrt(5x-1))

\int_{2}^{10} \frac{3}{5 x - 1} d x

integral from 2 to 4 of 1/(sqrt(x^2-4))

\int_{2}^{4} \frac{1}{x ^{2} - 4} d x

integral from 1 to 3 of 4x

\int_{1}^{3} 4 x d x

integral from-6 to 4 of 3/(x^4)

\int_{- 6}^{4} \frac{3}{x ^{4}} d x

integral from 0 to 8 of x^{2/3}

\int_{0}^{8} x^{\frac{2}{3}} d x

Frequently Asked Questions (FAQ)

What is the integral from 9 to 0 of |2x-9| ?
The integral from 9 to 0 of |2x-9| is -81/2