Evaluate $int_M(x-y^2+z^3)ds$

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Evaluate $int_M(x-y^2+z^3)ds$ when $M$ is a part of a cylinder $x^2+y^2=a^2$ where $a>0$ which in between the two plans, $x-z=0$ and $x+z=0$



So I did not manage to use green/gauss/stocks, so I tried to solve it as a surface integral.



first to find $|n|$ we use the parameterisation $phi(u,v)=(acos (u),asin (u),v)$



$phi_utimesphi_v=(acos(u),asin(u),0)$



So $|n|=a$



So the integral is $iint (a cos(u)-a^2sin^2(u)+v^3)adudv$ but I can I find the limit of integration? I know that $uin[0,2pi]$ and as for $v$ is is bounded by $x$ and $-x$



P.S or I can say that $F=nablacdot(fracx^22,-fracy^33,fracz^44)$ and so I can use gauss?




multivariable-calculus




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    Evaluate $int_M(x-y^2+z^3)ds$ when $M$ is a part of a cylinder $x^2+y^2=a^2$ where $a>0$ which in between the two plans, $x-z=0$ and $x+z=0$



    So I did not manage to use green/gauss/stocks, so I tried to solve it as a surface integral.



    first to find $|n|$ we use the parameterisation $phi(u,v)=(acos (u),asin (u),v)$



    $phi_utimesphi_v=(acos(u),asin(u),0)$



    So $|n|=a$



    So the integral is $iint (a cos(u)-a^2sin^2(u)+v^3)adudv$ but I can I find the limit of integration? I know that $uin[0,2pi]$ and as for $v$ is is bounded by $x$ and $-x$



    P.S or I can say that $F=nablacdot(fracx^22,-fracy^33,fracz^44)$ and so I can use gauss?




    multivariable-calculus




    share|cite|improve this question





















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      up vote
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      Evaluate $int_M(x-y^2+z^3)ds$ when $M$ is a part of a cylinder $x^2+y^2=a^2$ where $a>0$ which in between the two plans, $x-z=0$ and $x+z=0$



      So I did not manage to use green/gauss/stocks, so I tried to solve it as a surface integral.



      first to find $|n|$ we use the parameterisation $phi(u,v)=(acos (u),asin (u),v)$



      $phi_utimesphi_v=(acos(u),asin(u),0)$



      So $|n|=a$



      So the integral is $iint (a cos(u)-a^2sin^2(u)+v^3)adudv$ but I can I find the limit of integration? I know that $uin[0,2pi]$ and as for $v$ is is bounded by $x$ and $-x$



      P.S or I can say that $F=nablacdot(fracx^22,-fracy^33,fracz^44)$ and so I can use gauss?




      multivariable-calculus




      share|cite|improve this question











      Evaluate $int_M(x-y^2+z^3)ds$ when $M$ is a part of a cylinder $x^2+y^2=a^2$ where $a>0$ which in between the two plans, $x-z=0$ and $x+z=0$



      So I did not manage to use green/gauss/stocks, so I tried to solve it as a surface integral.



      first to find $|n|$ we use the parameterisation $phi(u,v)=(acos (u),asin (u),v)$



      $phi_utimesphi_v=(acos(u),asin(u),0)$



      So $|n|=a$



      So the integral is $iint (a cos(u)-a^2sin^2(u)+v^3)adudv$ but I can I find the limit of integration? I know that $uin[0,2pi]$ and as for $v$ is is bounded by $x$ and $-x$



      P.S or I can say that $F=nablacdot(fracx^22,-fracy^33,fracz^44)$ and so I can use gauss?





      multivariable-calculus





      share|cite|improve this question










      share|cite|improve this question




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