Question

How do you find `\int _ { - 2} ^ { 1} ( x - 8| x | ) d x`?

Answer 1

`int_(-2)^1(x-8|x|)dx =-43/2`

Explanation:

By definition of the integral we have that:

`int_(-2)^1(x-8|x|)dx = int_(-2)^0(x-8|x|)dx+int_0^1(x-8|x|)dx`

Now, in the first interval `|x|=-x`, while in the second `|x|=x`, so:

`int_(-2)^1(x-8|x|)dx = int_(-2)^0(x+8x)dx+int_0^1(x-8x)dx`

`int_(-2)^1(x-8|x|)dx = 9int_(-2)^0 xdx-7int_0^1xdx`

`int_(-2)^1(x-8|x|)dx = 9[x^2/2]_(-2)^0 - 7[x^2/2]_0^1=-18-7/2=-43/2`