## Related questions with answers

Question

Integrate f over the given region.

$f ( x , y ) = x ^ { 2 } + y ^ { 2 }$

over the triangular region with vertices (0, 0), (1, 0), and (0, 1)

Solutions

VerifiedSolution A

Solution B

Answered 1 year ago

Step 1

1 of 3We can define the triangular region as

$R = \left\{(x, y)\hspace{2mm}|\hspace{3mm} 0\leq y\leq 1-x, \hspace{2mm}0\leq x\leq 1\right\}$

Answered 1 year ago

Step 1

1 of 4As we can see in the image below, the given triangle is bounded by lines $x=0$ and $x=1$ from left and right, respectively, and by lines $y=0$ and $y=1-x$ from below and above, respectively.

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