Algebraic way to determine the bounds for double/triple integrals.

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So I was wondering, if we are given, say a double integral, where the bounds are in terms of x,y. Are there any algebraic ways to find what the bounds are for polar coordinates? I always just draw the region and then find the bounds from that, but I assume you can simply substitute the polar coordinates into the bounds and solve for $r$?What about $theta$?




integration polar-coordinates




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  • Do you have a simple example?
    – mvw
    Jul 25 at 21:39










  • @mvw Say the integral with bounds $y=sqrt1-(x-1)^2$ and $y=0$ and $x=0$ to $x=1$
    – Sorfosh
    Jul 26 at 9:50














up vote
2
down vote

favorite
1












So I was wondering, if we are given, say a double integral, where the bounds are in terms of x,y. Are there any algebraic ways to find what the bounds are for polar coordinates? I always just draw the region and then find the bounds from that, but I assume you can simply substitute the polar coordinates into the bounds and solve for $r$?What about $theta$?




integration polar-coordinates




share|cite|improve this question



















  • Do you have a simple example?
    – mvw
    Jul 25 at 21:39










  • @mvw Say the integral with bounds $y=sqrt1-(x-1)^2$ and $y=0$ and $x=0$ to $x=1$
    – Sorfosh
    Jul 26 at 9:50












up vote
2
down vote

favorite
1









up vote
2
down vote

favorite
1






1





So I was wondering, if we are given, say a double integral, where the bounds are in terms of x,y. Are there any algebraic ways to find what the bounds are for polar coordinates? I always just draw the region and then find the bounds from that, but I assume you can simply substitute the polar coordinates into the bounds and solve for $r$?What about $theta$?




integration polar-coordinates




share|cite|improve this question











So I was wondering, if we are given, say a double integral, where the bounds are in terms of x,y. Are there any algebraic ways to find what the bounds are for polar coordinates? I always just draw the region and then find the bounds from that, but I assume you can simply substitute the polar coordinates into the bounds and solve for $r$?What about $theta$?





integration polar-coordinates





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 25 at 21:26









Sorfosh

910616




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  • Do you have a simple example?
    – mvw
    Jul 25 at 21:39










  • @mvw Say the integral with bounds $y=sqrt1-(x-1)^2$ and $y=0$ and $x=0$ to $x=1$
    – Sorfosh
    Jul 26 at 9:50
















  • Do you have a simple example?
    – mvw
    Jul 25 at 21:39










  • @mvw Say the integral with bounds $y=sqrt1-(x-1)^2$ and $y=0$ and $x=0$ to $x=1$
    – Sorfosh
    Jul 26 at 9:50















Do you have a simple example?
– mvw
Jul 25 at 21:39




Do you have a simple example?
– mvw
Jul 25 at 21:39












@mvw Say the integral with bounds $y=sqrt1-(x-1)^2$ and $y=0$ and $x=0$ to $x=1$
– Sorfosh
Jul 26 at 9:50




@mvw Say the integral with bounds $y=sqrt1-(x-1)^2$ and $y=0$ and $x=0$ to $x=1$
– Sorfosh
Jul 26 at 9:50















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