Question

`int_0^50(x-abs(x))dx` how do I solve this?

Answer 1

See explanation.

Explanation:

First we can write the function `f(x)` as a piecewise function without the absolute value:

`f(x)={(x-x;x>=0),(x-(-x);x<0) :}`

If we simplify it we get:

`f(x)={(0;x>=0),(2x;x<0):}`

In the given interval `x in [0;50]` the function is constant `f(x)=0`, so the integral is:

`int_0^50f(x)dx=int_0^50 0dx=0`