Finding the area under and odd curve (1 Viewer)

[Born Dancer]

I dont get it!! the formula for finding the area under an odd curve is
b
| f(x) dx = 0
a
what does that mean!!?? how do i find the area? integrate on one side and double it?? Please help or direct me to a forum that can help!!

 

[rama_v]

Yes thats right, if you integrate an area under an odd curve you will get 0 (presuming that the limits are an equal distance away from the axis of symmetry of the curve, or else you will get some other incorrect answer). So what you do is you find the area under the one part and then double it. Alternatively you could split it up and find the area under the curve by adding it up (this is necessary for curves which are not odd)
I hope that made sense.

For example
Find the area under the curve y = x^3 between -2 and 2
You could either find the area from 0 to 2 and then double it, or you could integrate from -2 to 0, taking the absolute value, and then integrate from 0 to 2 and then add it on to your first answer. Both methods are correct.

 

[Born Dancer]

thankyou so much!! i did it wrong the first time but found the mistake. I'm now on the road to maths genius :uhhuh:

 

[Born Dancer]

the question is
Find the area under the curve y=x^3 - 4x between x=-2 and x=2

Following your advice, i integrate from 0 to 2 and double?? why do i get a negative answer??


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EDIT: don't worry... i found the answer.. from zero to two the curve is under the x axis. im guessing i should put it in absolute values..
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[acmilan]

the question is
Find the area under the curve y=x^3 - 4x between x=-2 and x=2

Following your advice, i integrate from 0 to 2 and double?? why do i get a negative answer??


______________________________________________________________
EDIT: don't worry... i found the answer.. from zero to two the curve is under the x axis. im guessing i should put it in absolute values..
_______________________________________

Correct, if a part of the curve is under the x-axis you need to evaluate that separately and take the absolute value