Area bounded by curves

  • Thread starter BOAS
  • Start date
  • #1
555
19
Hello,

quick question really.

Homework Statement



Find the area bound by the x axis, [itex]x = 1[/itex], [itex]x = 4[/itex] and [itex]y = 2/x[/itex]

Homework Equations





The Attempt at a Solution



Representing this graphically, the question is equivalent to performing the definite integral of [itex]y = 2/x[/itex] from [itex]1[/itex] to [itex]4[/itex]. Right?

Which would result in the area being equal to [itex]2 ln(4)[/itex]

It seems painfully obvious but this question has made me doubt myself so I wanted to check I haven't missed anything obvious... i.e is there any reason to do the longhand of subtracting the smaller areas from the larger ones.

Thanks,

BOAS
 

Answers and Replies

  • #2
52
7
You are absolutely correct. I see no reason to put anything more than the integral you described. For any positive, integrable function, the area between the curve and the x-axis is equal to the definite integral of the function over the region concerned.
 

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