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Write an iterated integral of a function f for the region given by a triangle with vertices at point (1,1), (1,2), (3,0).


I figured that I'm supposed to first find the equations of the three lines representing the sides of the triangle.

(1,2) and (1,1) make $x=1$

(1,1) and (3,0) make $y= -(1/2)x+(3/2)$

(1,2) and (3,0) make $y= -x+3$

Is that all I need to do? In other words, is my iterated integral the following?

$$ \int_{1}^3 \int_{\frac{1}{2}x+\frac{3}2}^{-x+3} f(x,y) dydx $$

It seems too simple and I'm afraid I'm missing something.

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Yep, it's as easy as that! Note that you got the slope of your second line wrong: it should be: $$ y = \frac{-1}{2}x + \frac{3}{2} $$

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  • $\begingroup$ Oh, error in typing on my part! Thank you for the correction and affirmation! $\endgroup$ – David Cardinal Nov 1 '14 at 22:48

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