the triangle is actually bounded by the lines, y = 2, y = -x + 2, and y = (1/2)x + 1/2
so your integral is:
1. where D: (0,2), (1,1), (3,2).
If you graph D you will see that its a triangle with base y = 2 and sides y = x and y = 1/2x + 1/2.
Our teacher doesen't want us splitting our integrals up into so you have to do this from x = y and x = 2y-1 so you get
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2. where D: x^2 + y^2 = 4.
If you graph D you will see that its a circle with radius 2
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letting u = 4- x^2 and du = -2x dx you get
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= -32 Where Did I go wrong? (answer should be 0)