Expert: Paul Klarreich - 1/19/2010

Question
I'm suppose to evaluate the definite integral for this..

f(x)= x if x<1
    1/x if x>or=1

{5
| f(x)dx
}-4


What i did here was try and doing
{0              {5
|       and     |
}-4             }1

I got
x^2/2 - x^2/2
=
0^2/2 - (-4^2/2)
= -8

then did,

ln5-ln1 = 1.609

I tried subtracting 1.609-(-8)
but it did not work and I tried a few different arrangements of those numbers and didn't get any answer right. Could you help me figure what I am doing wrong and then lead me in the right direction of what to do. Thanks


Answer
Questioner: brooke
Country: United States
Category: Calculus
Private: No
Subject: definite integral
Question: I'm suppose to evaluate the definite integral for this..

f(x)= x if   x < 1
     1/x if x >= 1

{5
| f(x)dx
}-4


What I did here was try and doing

That is TRY TO DO, please.  Don't embarrass your English teacher.



{0              {5
|       and     |
}-4             }1
........................
>> That should be:

{1              {5
| x    PLUS     | 1/x
}-4             }1

Since you are splitting your [-4 to 5] in two pieces, they must have a single 'split' point.  If you end the first at x = -1, you start the second there.
.......................

I got
x^2/2 from  -4 to 1.
=
(1)^2/2 - ((-4)^2/2)  << sloppy parenthesizing!!

1/2 - 8 = - 15/2

then did,

ln 5 - ln 1 = 1.609   << that looks OK.

I tried subtracting 1.609-(-8)
.......................
Fix things and try again.  You should be oK now.
.......................


but it did not work and I tried a few different arrangements of those numbers and didn't get any answer right. Could you help me figure what I am doing wrong and then lead me in the right direction of what to do. Thanks