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Popular >

integral from 1 to 6 of |x-3|

Solution

\int_{1}^{6} ∣ x - 3 ∣ d x

Solution

\frac{13}{2}

+1

Decimal Notation

6.5

Solution steps

\int_{1}^{6} ∣ x - 3 ∣ d x

Eliminate Absolutes

= \int_{1}^{3} - x + 3 d x + \int_{3}^{6} x - 3 d x

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

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

= 2 + \frac{9}{2}

Simplify

2 + \frac{9}{2} : \frac{13}{2}

= \frac{13}{2}

Popular Examples

integral from 0 to x of e^{-t^6}

\int_{0}^{x} e^{- t^{6}} d t

integral from 0 to 1 of e^{12x-11}

\int_{0}^{1} e^{12 x - 11} d x

integral from b to a of x^{11}

\int_{b}^{a} x^{11} d x

integral from 0 to 2sqrt(3 of) 1/(x^2+4)

\int_{0}^{23} \frac{1}{x ^{2} + 4} d x

integral from 0 to infinity of 4/(x^2+1)

\int_{0}^{\infty} \frac{4}{x ^{2} + 1} d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 6 of |x-3| ?
The integral from 1 to 6 of |x-3| is 13/2