jedai17
determine the limits and evaluate..
∫∫x2y2dA
where f is a figure bounded by F lines y = 1, y = 2 and x = 0, x = y
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electrokid
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|dw:1364052128248:dw|
that gives you the limits
electrokid
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it is easier to travel on y-axis because there is no sudden breaks
electrokid
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so \[0\le x\le y \qquad\text{&}\qquad1\le y\le2\]
electrokid
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if you are on the x-axis, you have to consider two pieces
A) \(1\le y\le2 \qquad\text{&}\qquad0\le x\le1\)
B) \(x\le y\le2 \qquad\text{&}\qquad1\le x\le2\)
and sum them
electrokid
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follow?
jedai17
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in x=y, the value of y will become a and 2?
electrokid
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"a"?
electrokid
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all points on the "x=y" line will have the same abscissa and ordinate
jedai17
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ah ok..
electrokid
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yup, in the problem, all you need are the limits
jedai17
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will i add these
A) 1≤y≤2&0≤x≤1
B) x≤y≤2&1≤x≤2 ??
electrokid
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use the first method its easier.
electrokid
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yes those are your two regions for the second method
jedai17
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x=0 to 1 and y= 1 to 2 ?
electrokid
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no
x=0 to y
and
y=1 to 2
electrokid
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|dw:1364053324530:dw|
jedai17
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i will integrate x^2y^2 using the limits x=0 to y
and
y=1 to 2 ?
electrokid
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methid "1" is the horizontal element
method "2" is the vertical
electrokid
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yep. you got it
jedai17
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ah ok..
in \[\int\limits_{1}^{2}\int\limits_{0}^{y} x^2y^2 dxdy\], got 127/36..
is it right?
electrokid
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\[
\int_{y=1}^2y^2\left[x^3\over3\right]_0^ydy={1\over3\times6}\left[y^6\right]_1^2
\]
jedai17
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7/2?
electrokid
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yep
electrokid
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.. wait..
jedai17
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ok..
electrokid
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false alarm
electrokid
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\[dA=dxdy\]
electrokid
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kapeesh?
jedai17
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127/36 = 3.53
7/2 = 3.5
my answer is 127/36 :)) its almost the same :)
electrokid
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lol
jedai17
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|dw:1364054668113:dw|
jedai17
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@electrokid ? look at my answer?
electrokid
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great job :D
I'd personally not like to have many terms while integrating ...
it gives migraine without it!
jedai17
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thank you!so is my answer also correct?
electrokid
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yep...
jedai17
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thank you! tnx for ur time :)
electrokid
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yer welcome :)