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  3. 1. evaluate the double integral for the function f

1. Evaluate the double integral for the function f(x,y) and the given region R. R is the rectangle...

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Advance Math

1. Evaluate the double integral for the functionf(x,y) and the given regionR.


R is the rectangle defined by-2  x  3 and1   y  e4

2. Evaluate the double integral

  f(x, y) dA
R

for the function f(x, y) and theregion R.

f(x, y) =

y
x3 + 9

; R is bounded by the lines

x = 1, y = 0, and y = x.

3. Find the average value of the functionf(x,y) over the plane regionR.

f(x, y) = xy; R isthe triangle bounded by y = x, y = 2 -x, and y = 0

4. Verify that y is a general solution of thedifferential equation and find a particular solution of thedifferential equation satisfying the initial condition.

y =

1
x2 − C

;  

dy
dx

= −2xy2;  y(0) = 7

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