The forum discussion centers on solving a double integration problem involving the integral $$\int\limits_{-2}^{\ 2} \ \int\limits_0^{\ \ \sqrt{4-x^2}} {x\over\sqrt{x^2+y^2} } \ dy \;dx$$. Participants suggest that the choice of substitution variable \( u = x^2 + y^2 \) is ineffective and recommend using polar coordinates instead. The discussion emphasizes the importance of understanding the geometric region of integration and the integrand's meaning, ultimately guiding the original poster toward a clearer path to the solution.
PREREQUISITESStudents and educators in calculus, particularly those focusing on multivariable calculus and integration techniques, as well as anyone seeking to improve their understanding of double integrals and polar coordinates.
BvU said:
it has no meaning , right ? the author just simply put inside the equation, right ?BvU said:
BvU said:
It's cos theta, so?BvU said:
chetzread said:
So ? Wouldn't substituting ##\theta## as integration variable be a sensible thing to try ?chetzread said:
ok, i got the ans now ...I'm wondering is this a special case? I have never learned and see this before ...BvU said:
？BvU said:
could you share your working with us ?chetzread said: