How do I determine the right boundarys for this Integral?
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Let $ G := {(x,y) in mathbb{R}^2 | -y<x<y^2, 0<y<1 } $
and $ B:= {(x,y) in mathbb{R}^2 | 0 leq y, x^2+ frac{y^2}{9} <1, x^2+y^2 >1 } $
And I want to integrate over some sort of function
$ int_G f(x) dx $ .
I was researching the hole day about methods of determining the right boundarys for a double integral.
I would be very greatful, if someone can help me getting there !
calculus real-analysis integration
asked Nov 21 at 15:01
wondering1123
10011
add a comment |
up vote
0
down vote
favorite
Let $ G := {(x,y) in mathbb{R}^2 | -y<x<y^2, 0<y<1 } $
and $ B:= {(x,y) in mathbb{R}^2 | 0 leq y, x^2+ frac{y^2}{9} <1, x^2+y^2 >1 } $
And I want to integrate over some sort of function
$ int_G f(x) dx $ .
I was researching the hole day about methods of determining the right boundarys for a double integral.
I would be very greatful, if someone can help me getting there !
calculus real-analysis integration
asked Nov 21 at 15:01
wondering1123
10011
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $ G := {(x,y) in mathbb{R}^2 | -y<x<y^2, 0<y<1 } $
and $ B:= {(x,y) in mathbb{R}^2 | 0 leq y, x^2+ frac{y^2}{9} <1, x^2+y^2 >1 } $
And I want to integrate over some sort of function
$ int_G f(x) dx $ .
I was researching the hole day about methods of determining the right boundarys for a double integral.
I would be very greatful, if someone can help me getting there !
calculus real-analysis integration
asked Nov 21 at 15:01
wondering1123
10011
Let $ G := {(x,y) in mathbb{R}^2 | -y<x<y^2, 0<y<1 } $
and $ B:= {(x,y) in mathbb{R}^2 | 0 leq y, x^2+ frac{y^2}{9} <1, x^2+y^2 >1 } $
And I want to integrate over some sort of function
$ int_G f(x) dx $ .
I was researching the hole day about methods of determining the right boundarys for a double integral.
I would be very greatful, if someone can help me getting there !
calculus real-analysis integration
calculus real-analysis integration
asked Nov 21 at 15:01
wondering1123
10011
asked Nov 21 at 15:01
wondering1123
10011
asked Nov 21 at 15:01
wondering1123
10011
asked Nov 21 at 15:01
wondering1123
10011
asked Nov 21 at 15:01
wondering1123
10011
10011
add a comment |
add a comment |
1 Answer
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Given a function $gcolonmathbb{R}^2tomathbb{R}, (x,y)mapsto g(x,y)$, then
$$
int_G g(x,y),dx,dy=int_0^1int_{-y}^{y^2} g(x,y),dx,dy=int_0^1left(int_{-y}^{y^2} g(x,y),dxright)dy
$$
answered Nov 21 at 15:25
francescop21
1,012115
oh wow..a little embarassing ^^ I thought of something else i guess...okay, the second one is screaming transformation with polarkoordinates :-)
– wondering1123
Nov 21 at 15:39
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Given a function $gcolonmathbb{R}^2tomathbb{R}, (x,y)mapsto g(x,y)$, then
$$
int_G g(x,y),dx,dy=int_0^1int_{-y}^{y^2} g(x,y),dx,dy=int_0^1left(int_{-y}^{y^2} g(x,y),dxright)dy
$$
answered Nov 21 at 15:25
francescop21
1,012115
oh wow..a little embarassing ^^ I thought of something else i guess...okay, the second one is screaming transformation with polarkoordinates :-)
– wondering1123
Nov 21 at 15:39
add a comment |
up vote
0
down vote
Given a function $gcolonmathbb{R}^2tomathbb{R}, (x,y)mapsto g(x,y)$, then
$$
int_G g(x,y),dx,dy=int_0^1int_{-y}^{y^2} g(x,y),dx,dy=int_0^1left(int_{-y}^{y^2} g(x,y),dxright)dy
$$
answered Nov 21 at 15:25
francescop21
1,012115
oh wow..a little embarassing ^^ I thought of something else i guess...okay, the second one is screaming transformation with polarkoordinates :-)
– wondering1123
Nov 21 at 15:39
add a comment |
up vote
0
down vote
up vote
0
down vote
Given a function $gcolonmathbb{R}^2tomathbb{R}, (x,y)mapsto g(x,y)$, then
$$
int_G g(x,y),dx,dy=int_0^1int_{-y}^{y^2} g(x,y),dx,dy=int_0^1left(int_{-y}^{y^2} g(x,y),dxright)dy
$$
answered Nov 21 at 15:25
francescop21
1,012115
Given a function $gcolonmathbb{R}^2tomathbb{R}, (x,y)mapsto g(x,y)$, then
$$
int_G g(x,y),dx,dy=int_0^1int_{-y}^{y^2} g(x,y),dx,dy=int_0^1left(int_{-y}^{y^2} g(x,y),dxright)dy
$$
answered Nov 21 at 15:25
francescop21
1,012115
answered Nov 21 at 15:25
francescop21
1,012115
answered Nov 21 at 15:25
francescop21
1,012115
answered Nov 21 at 15:25
francescop21
1,012115
1,012115
oh wow..a little embarassing ^^ I thought of something else i guess...okay, the second one is screaming transformation with polarkoordinates :-)
– wondering1123
Nov 21 at 15:39
add a comment |
oh wow..a little embarassing ^^ I thought of something else i guess...okay, the second one is screaming transformation with polarkoordinates :-)
– wondering1123
Nov 21 at 15:39
oh wow..a little embarassing ^^ I thought of something else i guess...okay, the second one is screaming transformation with polarkoordinates :-)
– wondering1123
Nov 21 at 15:39
oh wow..a little embarassing ^^ I thought of something else i guess...okay, the second one is screaming transformation with polarkoordinates :-)
– wondering1123
Nov 21 at 15:39
add a comment |
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