Evaluate
5\left(|m-2|+|m-1|+|m|\right)
Differentiate w.r.t. m
5\left(sign(m-2)+sign(m-1)+sign(m)\right)
Share
Copied to clipboard
\int |m|+|m-1|+|m-2|\mathrm{d}x
Evaluate the indefinite integral first.
\left(|m|+|m-1|+|m-2|\right)x
Find the integral of |m|+|m-1|+|m-2| using the table of common integrals rule \int a\mathrm{d}x=ax.
\left(|m|+|m-1|+|m-2|\right)\times 4-\left(|m|+|m-1|+|m-2|\right)\left(-1\right)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
5|m-1|+5|m|+5|m-2|
Simplify.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}