<p>f(x)=x if x<1
f(x)=1/x if x>=1</p>
<p>find integral f(x) dx from -4 to 6.</p>
<p>This is what I did:
integral f(x) dx from -4 to 6.
=F(6)-F(-4)
=ln(6)-(8)
=-6.208</p>
<p>But according the answer at the back of the book, this is incorrect. I don't understand where went wrong. So, can anyone give me any hints on where I did wrong. Thanks.</p>
<p>You have to do 2 seperate integrals.
from -4 to 0 the area is under the x axis. The area = 1/2<em>4</em>4 = 8 units. From 0 to 1 it is 1/2<em>1</em>1 = .5 units. It is a straight line, just use triangles.
Then from 1 to 6
ln(6) - ln(1) = ln(6). The total areas are 8 + .5 + ln(6)
Now, depending on what type of problem this is, you may need the net area, in which case you make 8 negative, and get around -5.5. You have to decide based on the problem if you need the net area, or total area on both sides of the x axis.</p>