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About $displaystyleint_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$?



The 2019 Stack Overflow Developer Survey Results Are In
Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraSurface integral over an inconvenient surfaceFinding volume between plane and paraboloidConvolution integralCan this integral be computed in closed-form?Compute the following triple integral on an ellipsoidEquivalent normal vectors to a surfaceCalculate $ int_gamma omega$ where $ omega(x,y)=frac-ydx+xdyx^2+y^2 $compute $int_Qfrac1 , dx$ on $Q=[0,1]^2$Evaluate $int_0^1 int_0^1 int_0^1 frac1x^2+y^2+z^2dxdydz$On the integral $iint_partial B_1(0)fracdOmegaleft(1+acdot rright)left(1+bcdot rright)$










1












$begingroup$


An integral has been pushed me over the edge for several weeks. It reads as:
$$displaystyleint_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$



I tried to calculate the surface integral inside using spherical coordinates, but it seems that I couldn't do any further calculation since the integrand function is something like
$$e^-big(k_1(varphi)sin^2theta+k_2(varphi)cos^2theta+k_3(varphi)sinthetacosthetabig)sintheta .$$
Then I tried to use variable substitution to compute, similarly, I didn't get anything useful. I was also trying to use Maple to compute, but it didn't work at all. My original intention is to prove that the formula
$$displaystyle e^^2int_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$
is bounded.



I would be grateful if you could give me a definite result.@Sos404










share|cite|improve this question









$endgroup$
















    1












    $begingroup$


    An integral has been pushed me over the edge for several weeks. It reads as:
    $$displaystyleint_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$



    I tried to calculate the surface integral inside using spherical coordinates, but it seems that I couldn't do any further calculation since the integrand function is something like
    $$e^-big(k_1(varphi)sin^2theta+k_2(varphi)cos^2theta+k_3(varphi)sinthetacosthetabig)sintheta .$$
    Then I tried to use variable substitution to compute, similarly, I didn't get anything useful. I was also trying to use Maple to compute, but it didn't work at all. My original intention is to prove that the formula
    $$displaystyle e^^2int_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$
    is bounded.



    I would be grateful if you could give me a definite result.@Sos404










    share|cite|improve this question









    $endgroup$














      1












      1








      1





      $begingroup$


      An integral has been pushed me over the edge for several weeks. It reads as:
      $$displaystyleint_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$



      I tried to calculate the surface integral inside using spherical coordinates, but it seems that I couldn't do any further calculation since the integrand function is something like
      $$e^-big(k_1(varphi)sin^2theta+k_2(varphi)cos^2theta+k_3(varphi)sinthetacosthetabig)sintheta .$$
      Then I tried to use variable substitution to compute, similarly, I didn't get anything useful. I was also trying to use Maple to compute, but it didn't work at all. My original intention is to prove that the formula
      $$displaystyle e^^2int_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$
      is bounded.



      I would be grateful if you could give me a definite result.@Sos404










      share|cite|improve this question









      $endgroup$




      An integral has been pushed me over the edge for several weeks. It reads as:
      $$displaystyleint_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$



      I tried to calculate the surface integral inside using spherical coordinates, but it seems that I couldn't do any further calculation since the integrand function is something like
      $$e^-big(k_1(varphi)sin^2theta+k_2(varphi)cos^2theta+k_3(varphi)sinthetacosthetabig)sintheta .$$
      Then I tried to use variable substitution to compute, similarly, I didn't get anything useful. I was also trying to use Maple to compute, but it didn't work at all. My original intention is to prove that the formula
      $$displaystyle e^^2int_mathbbR_y^3int_mathbbS^2e^x-[(x-y)cdotomega]omegadomega dy$$
      is bounded.



      I would be grateful if you could give me a definite result.@Sos404







      real-analysis integration multivariable-calculus






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 24 at 17:22









      LinxiaodiuLinxiaodiu

      111




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