Expert: Paul Klarreich - 3/30/2008

Question
How can I solve this piece wise function?
Let f(x)= {3,     x ≤ 3
         {6 - x, x > 3

Use geometric formulas to find  ∫6
                                1 f(x) dx

Answer
Questioner:   kayla
Category:  Calculus
Private:  No
 
Subject:  ap calculus
Question:  How can I solve this piece wise function?
Let f(x)= {3,     x ≤ 3
        {6 - x, x > 3

Use geometric formulas to find  ∫6
                               1 f(x) dx
..........................................
Hi, Kayla,
First you have to know what th definition SAYS:
 
 
f(x)= {3,    WHEN  x ≤ 3
     {6 - x,WHEN x > 3

So you would draw, from x = 1 to 3, the horizontal line y = 3 and see a rectangle -- 2 wide, 3 high, area 6.

And you would draw, from x = 3 to 6, the line going from y = 6-3=3 to y = 6-6=0,
and see a triangle, base = 3, height = 3, A = 9/2

Put them together.