How do I calculate this integral? $$\iint_D x\,dx\,dy$$ where $$ D = \left\{ (x,y)\in \mathbb{R}^2 : 4x^2+y^2 \leq 1,\ 2y+4x^2-1 \leq 0 \right\} $$
How do I calculate this restricted integral?
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calculus
real-analysis
integration
functional-analysis
analysis
1 Answers
5
The integral is zero since your function is odd in $x$, and your domain is symmetric with respect to the line $x=0$.