Mixing
$int_{phi} z^2e^{z^3}sin z$ dz
0
$begingroup$
$int_{phi} z^2e^{z^3}sin z$ dz where $phi in [0, 2pi]$ and $ phi (t) =e^{4it}$.
I want to use Cauchy's Integral Formuła for Derivtives, but I can't simplify this expression. I use substitution $ z=e^{4it}$ and $dz=ie^{4it}$ dt.
integration complex-analysis
edited Jan 20 at 6:28
stone-zeng
210210
asked Jan 19 at 23:01
KamiloKamilo
43
$endgroup$
add a comment |
0
$begingroup$
$int_{phi} z^2e^{z^3}sin z$ dz where $phi in [0, 2pi]$ and $ phi (t) =e^{4it}$.
I want to use Cauchy's Integral Formuła for Derivtives, but I can't simplify this expression. I use substitution $ z=e^{4it}$ and $dz=ie^{4it}$ dt.
integration complex-analysis
edited Jan 20 at 6:28
stone-zeng
210210
asked Jan 19 at 23:01
KamiloKamilo
43
$endgroup$
5
$begingroup$
$z^2e^{z^3}sin(z)$ is holomorphic in and on the circle $z=e^{i4t}$, $tin [0,pi/2]$. The integral is $0$ by Cauchy's Integral Theorem.
$endgroup$
– Mark Viola
Jan 19 at 23:08
$begingroup$
Do should I use any any another way?
$endgroup$
– Kamilo
Jan 19 at 23:19
2
$begingroup$
Why would you want to proceed any other way when the conclusion is immediate here?
$endgroup$
– Mark Viola
Jan 20 at 1:03
add a comment |
0
0
0
$begingroup$
$int_{phi} z^2e^{z^3}sin z$ dz where $phi in [0, 2pi]$ and $ phi (t) =e^{4it}$.
I want to use Cauchy's Integral Formuła for Derivtives, but I can't simplify this expression. I use substitution $ z=e^{4it}$ and $dz=ie^{4it}$ dt.
integration complex-analysis
edited Jan 20 at 6:28
stone-zeng
210210
asked Jan 19 at 23:01
KamiloKamilo
43
$endgroup$
$int_{phi} z^2e^{z^3}sin z$ dz where $phi in [0, 2pi]$ and $ phi (t) =e^{4it}$.
I want to use Cauchy's Integral Formuła for Derivtives, but I can't simplify this expression. I use substitution $ z=e^{4it}$ and $dz=ie^{4it}$ dt.
integration complex-analysis
integration complex-analysis
edited Jan 20 at 6:28
stone-zeng
210210
asked Jan 19 at 23:01
KamiloKamilo
43
edited Jan 20 at 6:28
stone-zeng
210210
asked Jan 19 at 23:01
KamiloKamilo
43
edited Jan 20 at 6:28
stone-zeng
210210
edited Jan 20 at 6:28
stone-zeng
210210
edited Jan 20 at 6:28
stone-zeng
210210
210210
asked Jan 19 at 23:01
KamiloKamilo
43
asked Jan 19 at 23:01
KamiloKamilo
43
asked Jan 19 at 23:01
KamiloKamilo
43
43
5
$begingroup$
$z^2e^{z^3}sin(z)$ is holomorphic in and on the circle $z=e^{i4t}$, $tin [0,pi/2]$. The integral is $0$ by Cauchy's Integral Theorem.
$endgroup$
– Mark Viola
Jan 19 at 23:08
$begingroup$
Do should I use any any another way?
$endgroup$
– Kamilo
Jan 19 at 23:19
2
$begingroup$
Why would you want to proceed any other way when the conclusion is immediate here?
$endgroup$
– Mark Viola
Jan 20 at 1:03
add a comment |
5
$begingroup$
$z^2e^{z^3}sin(z)$ is holomorphic in and on the circle $z=e^{i4t}$, $tin [0,pi/2]$. The integral is $0$ by Cauchy's Integral Theorem.
$endgroup$
– Mark Viola
Jan 19 at 23:08
$begingroup$
Do should I use any any another way?
$endgroup$
– Kamilo
Jan 19 at 23:19
2
$begingroup$
Why would you want to proceed any other way when the conclusion is immediate here?
$endgroup$
– Mark Viola
Jan 20 at 1:03
5
5
$begingroup$
$z^2e^{z^3}sin(z)$ is holomorphic in and on the circle $z=e^{i4t}$, $tin [0,pi/2]$. The integral is $0$ by Cauchy's Integral Theorem.
$endgroup$
– Mark Viola
Jan 19 at 23:08
$begingroup$
$z^2e^{z^3}sin(z)$ is holomorphic in and on the circle $z=e^{i4t}$, $tin [0,pi/2]$. The integral is $0$ by Cauchy's Integral Theorem.
$endgroup$
– Mark Viola
Jan 19 at 23:08
$begingroup$
Do should I use any any another way?
$endgroup$
– Kamilo
Jan 19 at 23:19
$begingroup$
Do should I use any any another way?
$endgroup$
– Kamilo
Jan 19 at 23:19
2
2
$begingroup$
Why would you want to proceed any other way when the conclusion is immediate here?
$endgroup$
– Mark Viola
Jan 20 at 1:03
$begingroup$
Why would you want to proceed any other way when the conclusion is immediate here?
$endgroup$
– Mark Viola
Jan 20 at 1:03
add a comment |
0
active
oldest
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5
$begingroup$
$z^2e^{z^3}sin(z)$ is holomorphic in and on the circle $z=e^{i4t}$, $tin [0,pi/2]$. The integral is $0$ by Cauchy's Integral Theorem.
$endgroup$
– Mark Viola
Jan 19 at 23:08
$begingroup$
Do should I use any any another way?
$endgroup$
– Kamilo
Jan 19 at 23:19
2
$begingroup$
Why would you want to proceed any other way when the conclusion is immediate here?
$endgroup$
– Mark Viola
Jan 20 at 1:03