Question

f(x)= |x|/x for x cannot equal 0 and 0 for x=0

the value from integral -5 to 3f(x)dx is
-2?

How do I get the graph of this without using a calculator and solve for this

Answer 1

|x|/x = 1 for x>0
|x|/x = -1 for x<0
f(x) is just two horizontal lines, below and above the x-axis .

So, the integral from -5 to 3 is just the area of a 5x1 rectangle below the x-axis subtracted from that of a 3x1 rectangle above the x-axis.

Answer 2

where did you get 1 and -1 why do they equal that

Answer 3

recall the definition of |x|

|x| = x if x >= 0
|x| = -x if x < 0

When you divide by x, that just gives you 1 and -1

Go online to any handy graphing web site, and have it do the graph for you.