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

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

R is the rectangle defined by -2 x 3 and 1 y e⁴

2. Evaluate the double integral

	f(x, y) dA

R

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

f(x, y) =

x³ + 9

; R is bounded by the lines

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

3. Find the average value of the function f(x,y) over the plane region R.

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

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

y =

x² − C

;

= −2xy²; y(0) = 7

Solutions

Expert Solution

If you have any doubts please ask me in comments

In 1st question you give me only f so i only put limit and not evaluated the integral because f is not given ...

Last question in verification i didi with two method

Colby Messinger answered 11 months ago

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