Integrating the Area between Two Graphs - Positive & Negative Regions

[quietrain]

hi, erm i just want to ask about integration

lets say for finding area between 2 graphs, on the positive region, we take the integration of upper curve minus the lower curve w.r.t x-axis

so what about the area under the x-axis (negative part)

do we take the more negative curve(greater negative w.r.t x-axis, meaning further away from x-axis) minus the less negative curve(less negative w.r.t x-axis, meaning closer to x-axis) or is it the other way round?

also what will be my integration limits from? like -5 to -3 or -3 to -5 ?

also is this the same w.r.t y-axis?

thanks

 

[sreeram]

Bigger area minus smaller area will give the positive area. Also limits from -5 to -3 or -3 to -5 is optional.If Integral value from -5 to -3 is positive, then integral from -3 to -5 will be negative. Whatever way you do the integration, if you are finding the area, then take only the positive value

 

[quietrain]

also, if let's say, above the x-axis,

curve A is above curve B w.r.t x-axis, but curve A extends to below the x-axis AND is closer to the x-axis then curve B,

so what will i have to integrate from?

i know on top is integrate curve A - B, but do i take the limits of x-values, all the way from the part where the graph is positive, to including the negative graph part?

or do i have to integrate only the positive part separately, and then integrate the negative by itself?

 

[sreeram]

You will have to do separate integration. If you take the limit all the way, then the area that you get will be the area of curve above x axis minus area of curve below x axis. So you should separately take the limits.

For example, integral f(x)= sin(x) from 0 to 360 degrees is zero. This is because the area of curve above x axis(from 0 to 180) is equal to area of curve below x-axis as is clear from its symmetry. The areas get subtracted to give zero as the answer.

 

[quietrain]

oh isee...

so should i take the more negative curve - the less negative curve or the other way round? if i want to find the area of the region bounded by the negative curves.