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Popular >

integral from 0 to 12 of |x-9|

Solution

\int_{0}^{12} ∣ x - 9 ∣ d x

Solution

45

Solution steps

\int_{0}^{12} ∣ x - 9 ∣ d x

Eliminate Absolutes

= \int_{0}^{9} - x + 9 d x + \int_{9}^{12} x - 9 d x

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

\int_{9}^{12} x - 9 d x = \frac{9}{2}

= \frac{81}{2} + \frac{9}{2}

Simplify

\frac{81}{2} + \frac{9}{2} : 45

= 45

Popular Examples

integral from 1 to 3 of (4x^4+1)/(4x^2)

\int_{1}^{3} \frac{4 x ^{4} + 1}{4 x ^{2}} d x

integral from 6 to sin(x) of x^3

\int_{6}^{s i n (x)} x^{3} d x

integral from 0 to 4 of (x-6)^2

\int_{0}^{4} (x - 6)^{2} d x

integral from x to y of ln(sin(t))

\int_{x}^{y} ln (sin (t)) d t

integral from-pi to pi of cos(t)

\int_{- π}^{π} cos (t) d t

Frequently Asked Questions (FAQ)

What is the integral from 0 to 12 of |x-9| ?
The integral from 0 to 12 of |x-9| is 45