Double Integral in Rectangular Coordinates

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SUMMARY

The discussion focuses on solving a double integral in rectangular coordinates, specifically the integral from 0 to 5 of the integral from 0 to 5y of 8e^(y^2)dxdy. The user correctly identifies that there is no elementary antiderivative for e^(y^2) but notes that a substitution can simplify the problem. The recommended substitution is u=y^2, which allows for the integration of y*e^(y^2). This approach is essential for progressing in the solution of the integral.

PREREQUISITES
  • Understanding of double integrals in rectangular coordinates
  • Familiarity with substitution methods in integration
  • Knowledge of the properties of exponential functions
  • Basic calculus concepts, including antiderivatives
NEXT STEPS
  • Learn about substitution techniques in integration
  • Study the properties of the Gaussian integral
  • Explore numerical methods for evaluating integrals without elementary antiderivatives
  • Review advanced integration techniques, including integration by parts
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques, as well as educators seeking to enhance their understanding of double integrals and substitution methods.

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Homework Statement



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Homework Equations



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The Attempt at a Solution


I set up the intgral at
integral from 0 to 5 of integral from 0 to 5y of 8e^(y^2)dxdy

I solved it as an iterated integral so I solved the first part, then ended up with integral from 0 to 5 of 40ye^(y^2)

Am I going about it right? Isn't there no antideriative for e^(y^2)? I don't know where to go from here in solving this

Thanks everyone.
 
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Yes, there's no elementary antiderivative for e^(y^2). There is one for y*e^(y^2). Use the substitution u=y^2.
 

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