Need help with complex integration
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(a) Let $mathcal C$ be the triangle with vertices at $0,1,i$ oriented counterclockwise. Calculate
$$int_mathcal C|z|^2,dz.$$
(b) Evaluate
$$int_mathcal Cz^3e^-z^4,dz$$
along the path
$$mathcal C=leftsin t^2-ifrac2t^2pi:0le tlesqrtpi/2right.$$
(c) Evaluate
$$oint_=pifracsin zz^2(z-pi/2),dz.$$
I'm not sure if I need to integrate over the $ito0$ and $0to1$ line segments as well.
complex-analysis complex-integration
edited Aug 16 at 4:13
Parcly Taxel
33.6k136588
asked Aug 16 at 3:50
bigbloakers
33
add a comment |Â
up vote
-1
down vote
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(a) Let $mathcal C$ be the triangle with vertices at $0,1,i$ oriented counterclockwise. Calculate
$$int_mathcal C|z|^2,dz.$$
(b) Evaluate
$$int_mathcal Cz^3e^-z^4,dz$$
along the path
$$mathcal C=leftsin t^2-ifrac2t^2pi:0le tlesqrtpi/2right.$$
(c) Evaluate
$$oint_=pifracsin zz^2(z-pi/2),dz.$$
I'm not sure if I need to integrate over the $ito0$ and $0to1$ line segments as well.
complex-analysis complex-integration
edited Aug 16 at 4:13
Parcly Taxel
33.6k136588
asked Aug 16 at 3:50
bigbloakers
33
It is more accurate to say "the value of the integral $is$ " rather than "the value of the integral $becomes$" .
– DanielWainfleet
Aug 16 at 7:40
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
(a) Let $mathcal C$ be the triangle with vertices at $0,1,i$ oriented counterclockwise. Calculate
$$int_mathcal C|z|^2,dz.$$
(b) Evaluate
$$int_mathcal Cz^3e^-z^4,dz$$
along the path
$$mathcal C=leftsin t^2-ifrac2t^2pi:0le tlesqrtpi/2right.$$
(c) Evaluate
$$oint_=pifracsin zz^2(z-pi/2),dz.$$
I'm not sure if I need to integrate over the $ito0$ and $0to1$ line segments as well.
complex-analysis complex-integration
edited Aug 16 at 4:13
Parcly Taxel
33.6k136588
asked Aug 16 at 3:50
bigbloakers
33
(a) Let $mathcal C$ be the triangle with vertices at $0,1,i$ oriented counterclockwise. Calculate
$$int_mathcal C|z|^2,dz.$$
(b) Evaluate
$$int_mathcal Cz^3e^-z^4,dz$$
along the path
$$mathcal C=leftsin t^2-ifrac2t^2pi:0le tlesqrtpi/2right.$$
(c) Evaluate
$$oint_=pifracsin zz^2(z-pi/2),dz.$$
I'm not sure if I need to integrate over the $ito0$ and $0to1$ line segments as well.
complex-analysis complex-integration
edited Aug 16 at 4:13
Parcly Taxel
33.6k136588
asked Aug 16 at 3:50
bigbloakers
33
edited Aug 16 at 4:13
Parcly Taxel
33.6k136588
edited Aug 16 at 4:13
Parcly Taxel
33.6k136588
edited Aug 16 at 4:13
Parcly Taxel
33.6k136588
33.6k136588
asked Aug 16 at 3:50
bigbloakers
33
asked Aug 16 at 3:50
bigbloakers
33
asked Aug 16 at 3:50
bigbloakers
33
33
It is more accurate to say "the value of the integral $is$ " rather than "the value of the integral $becomes$" .
– DanielWainfleet
Aug 16 at 7:40
add a comment |Â
It is more accurate to say "the value of the integral $is$ " rather than "the value of the integral $becomes$" .
– DanielWainfleet
Aug 16 at 7:40
It is more accurate to say "the value of the integral $is$ " rather than "the value of the integral $becomes$" .
– DanielWainfleet
Aug 16 at 7:40
It is more accurate to say "the value of the integral $is$ " rather than "the value of the integral $becomes$" .
– DanielWainfleet
Aug 16 at 7:40
add a comment |Â
1 Answer
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You have only integrated over the line segment $ 1 to i$. You have to integrate over the the line segments $i→0$ and $0→1$ as well.
Then you have to add the three resulting integrals.
answered Aug 16 at 6:52
Fred
38k1238
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
You have only integrated over the line segment $ 1 to i$. You have to integrate over the the line segments $i→0$ and $0→1$ as well.
Then you have to add the three resulting integrals.
answered Aug 16 at 6:52
Fred
38k1238
add a comment |Â
up vote
1
down vote
accepted
You have only integrated over the line segment $ 1 to i$. You have to integrate over the the line segments $i→0$ and $0→1$ as well.
Then you have to add the three resulting integrals.
answered Aug 16 at 6:52
Fred
38k1238
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
You have only integrated over the line segment $ 1 to i$. You have to integrate over the the line segments $i→0$ and $0→1$ as well.
Then you have to add the three resulting integrals.
answered Aug 16 at 6:52
Fred
38k1238
You have only integrated over the line segment $ 1 to i$. You have to integrate over the the line segments $i→0$ and $0→1$ as well.
Then you have to add the three resulting integrals.
answered Aug 16 at 6:52
Fred
38k1238
answered Aug 16 at 6:52
Fred
38k1238
answered Aug 16 at 6:52
Fred
38k1238
answered Aug 16 at 6:52
Fred
38k1238
38k1238
add a comment |Â
add a comment |Â
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It is more accurate to say "the value of the integral $is$ " rather than "the value of the integral $becomes$" .
– DanielWainfleet
Aug 16 at 7:40