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Popular >

integral from 0 to 6 of |x-3|

Solution

\int_{0}^{6} ∣ x - 3 ∣ d x

Solution

9

Solution steps

\int_{0}^{6} ∣ x - 3 ∣ d x

Eliminate Absolutes

= \int_{0}^{3} - x + 3 d x + \int_{3}^{6} x - 3 d x

\int_{0}^{3} - x + 3 d x = \frac{9}{2}

\int_{3}^{6} x - 3 d x = \frac{9}{2}

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

Simplify

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

= 9

Graph

Popular Examples

integral from-1 to 1 of (e^x)/(e^x+1)

\int_{- 1}^{1} \frac{e ^{x}}{e ^{x} + 1} d x

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

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

integral from 0 to 1 of x*arctan(x)

\int_{0}^{1} x \cdot arctan (x) d x

integral from-2 to 7 of 1/((x+1)^{2/3)}

\int_{- 2}^{7} \frac{1}{( x + 1 ) ^{\frac{2}{3}}} d x

integral from 4 to 8 of x/(sqrt(x^2-15))

\int_{4}^{8} \frac{x}{x ^{2} - 15} d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of |x-3| ?
The integral from 0 to 6 of |x-3| is 9