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Integration rule query

When you have two curves and you're told to find the area under them, how do you know which one to subtract from the other ? I was told you do the lower one subtracted from the higher one, but that didn't make any sense to me .

Eg: For this one, how do you know which side you take everything to ?



I got the answer right ,by moving everything to the left after equating, just not sure. Or does it not matter the way you do it ?
Reply 1
Avatar for the bear
the bear
20
it shouldn't really matter which one you subtract from the other... one way will give you a negative answer...just make it positive :wink:

the baer

:banana2::badger::banana2:
Reply 2
Avatar for dknt
dknt
12
Original post by WildBerry
When you have two curves and you're told to find the area under them, how do you know which one to subtract from the other ? I was told you do the lower one subtracted from the higher one, but that didn't make any sense to me .

Eg: For this one, how do you know which side you take everything to ?



I got the answer right ,by moving everything to the left after equating, just not sure. Or does it not matter the way you do it ?


Try to imagine shapes in your head. To get that shape you need a larger shape minus a smaller shape, so you need to integrate the curve that gives the top side of the curve, minus the integral of the curve that gives the bottom side of the shape.
(edited 13 years ago)
Reply 3
Avatar for Pheylan
Pheylan
integrating the top one gives the area under the top one

integrating the bottom one gives the area under the bottom one

you want the area between them

so top-bottom
As the bear said, it doesn't matter which you take from which, it's the magnitude (absolute value) of the area that's important.

More strictly, if you want to find the area between two curves f(x) and g(x) which intersect at points x=a and x=b, you would evaluate:

Area=∣∫ab(f(x)−g(x))dx∣Area = |\int_a^b (f(x)-g(x)) dx|

The principle is the most important thing here, though.
Reply 5
Avatar for WildBerry
WildBerry
OP
Thanks everyone :smile:

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