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C4 integration question...

I really don't understand what this question is asking you to do please could someone explain for me!

The finite region bouded by the curve with equation y= (1/(x-3))-(1/(x-1)) and the lines x=4 and y=0.25 is denoted by R. Show that the area of R is
ln(3/2)-0.25.

Thanks. :smile:

Reply 1

Gaz031

This might help.
http://img300.echo.cx/img300/5185/swscan000046ur.jpg
Basically the stipulation is that the area R is to the right of x=4 and above y=0.25 (as otherwise the area would be infinite). Clearly y=0.25 at x=5 and there is no area above y=0.25 at x>5, so x=5 is the upper limit on the first integral.
The second integral subtracts the area below the line y=0.25 for 4<x<5, as the first integral finds the area bounded by the curve and x axis [note you could also have simply found the area of the rectangle instead of doing an integra[.