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Popular >

integral from 0 to 6 of |x-5|

Solution

\int_{0}^{6} ∣ x - 5 ∣ d x

Solution

13

Solution steps

\int_{0}^{6} ∣ x - 5 ∣ d x

Eliminate Absolutes

= \int_{0}^{5} - x + 5 d x + \int_{5}^{6} x - 5 d x

\int_{0}^{5} - x + 5 d x = \frac{25}{2}

\int_{5}^{6} x - 5 d x = \frac{1}{2}

= \frac{25}{2} + \frac{1}{2}

Simplify

\frac{25}{2} + \frac{1}{2} : 13

= 13

Popular Examples

integral from-1 to 2 of (2x+5)

\int_{- 1}^{2} (2 x + 5) d x

integral from 0 to ln(5) of 2e^{2x}

\int_{0}^{l n (5)} 2 e^{2 x} d x

integral from 0 to 2pi of (cos(x))^4

\int_{0}^{2 π} (cos (x))^{4} d x

integral from-2 to 0 of 1/((2-1)^3)

\int_{- 2}^{0} \frac{1}{( 2 - 1 ) ^{3}} d x

integral from-7 to 3 of |x|

\int_{- 7}^{3} ∣ x ∣ d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 6 of |x-5| ?
The integral from 0 to 6 of |x-5| is 13