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Popular >

integral from 0 to 4 of |x-1|

Solution

\int_{0}^{4} ∣ x - 1 ∣ d x

Solution

5

Solution steps

\int_{0}^{4} ∣ x - 1 ∣ d x

Eliminate Absolutes

= \int_{0}^{1} - x + 1 d x + \int_{1}^{4} x - 1 d x

\int_{0}^{1} - x + 1 d x = \frac{1}{2}

\int_{1}^{4} x - 1 d x = \frac{9}{2}

= \frac{1}{2} + \frac{9}{2}

Simplify

\frac{1}{2} + \frac{9}{2} : 5

= 5

Graph

Popular Examples

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

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

integral from 0 to 2 of x^3sqrt(16-x^4)

\int_{0}^{2} x^{3} 16 - x^{4} d x

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

\int_{0}^{3} \frac{x}{1 + 1 + x} d x

integral from 0 to infinity of ln(x)

\int_{0}^{\infty} ln (x) d x

integral from 1/2 to 1 of e^{sqrt(2x-1)}

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of |x-1| ?
The integral from 0 to 4 of |x-1| is 5