anonymous
  • anonymous
find the volume of the given solid: under the surface z=2x+y^2 and above the triangle vertices (1,1),(4,1) and (1,2).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1360708771803:dw|
TuringTest
  • TuringTest
what is the equation of this part of the area?|dw:1360709404014:dw|
anonymous
  • anonymous
y=2x?

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TuringTest
  • TuringTest
no,you can see that the slope from x=1 to x=4 is down for that part of the graph, so the coefficient of x will be negative you should use point-slope form way back from algebra I to do this|dw:1360709566120:dw|
anonymous
  • anonymous
@TuringTest yes i can see that
anonymous
  • anonymous
so -1/3?
TuringTest
  • TuringTest
yes, so now use point-slope form on either point \((x_0,y_0)\) to get the equation of the line \[y-y_0=-\frac13(x-x_0)\]
anonymous
  • anonymous
y-1 = -1/3 (x-1)?
TuringTest
  • TuringTest
no, because (1,1) is not one of the points on the diagonal line
anonymous
  • anonymous
ok
anonymous
  • anonymous
the only one that i can use the (1,2) and (1,4)
TuringTest
  • TuringTest
correct, we are using point-slope form on the diagonal line, so we can only get the equation from points that lie \(on\) the line.
anonymous
  • anonymous
y-2= -1/3 (x-1)
TuringTest
  • TuringTest
yes, now solve for y...
anonymous
  • anonymous
y= -1/3x+1/3 (+2) y=-1/3 x+7/3
TuringTest
  • TuringTest
yes, and now you need the line that bounds the region below:|dw:1360710827125:dw|
anonymous
  • anonymous
same using slope
TuringTest
  • TuringTest
er, yeah you could, but you should really be able to eyeball this one. Note here that all we have been doing so far is basic algebra to find the equations of the bounds of the region. Just because you are in calc2 does not mean you can forget the basics!! On the contrary, here is where you actually need them most.
anonymous
  • anonymous
really is calc 3
TuringTest
  • TuringTest
Well, what some people call cal3 others call calc2. MIT for instance only has 2 basic calc classes: single and multivariable. But enough semantics, what's the equation of the bottom line?
anonymous
  • anonymous
@TuringTest is 1?
TuringTest
  • TuringTest
y=1, yes so y is bound by the two equations we found, so they will be the bounds for the inner integral, which will be with respect to x. what are the bounds on x, which we will use for the outer integral.
anonymous
  • anonymous
x=1, 4 and y= 1 , 1/3x+7/3?
TuringTest
  • TuringTest
yes :)
anonymous
  • anonymous
\[\int\limits_{1}^{4} \int\limits_{1}^{1/3x+7/3} xy \] dy dx
TuringTest
  • TuringTest
the integrand is the function for z, so use that, not xy gotta go, happy integrating!
anonymous
  • anonymous
@TuringTest thank you so much
anonymous
  • anonymous
sorry is not z=2x+y^2 i just mistype the book is really saying xy

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