The discussion centers on the double integral \int^1_0 \int^1_y sin(x^2) dx dy and the challenges faced in integrating it. The user initially attempts to reverse the order of integration to \int^1_0 \int^1_x sin(x^2) dy dx, but encounters difficulties. A correction is suggested, leading to the proper bounds of \int^1_0 \int^x_0, which simplifies the integral to \int^1_0 x sin(x^2) dx. The final evaluation yields -1/2 cos (x^2) | 1_0, confirming the solution.
sin(x^2)Students studying calculus, particularly those focusing on double integrals and integration techniques, as well as educators looking for examples of common pitfalls in integration problems.
Your limits in the new double integral is incorrect. If in doubt, look at the original double integral and draw a picture of the region enclosed by the limits. Then try to express the limits of the double integral in the reversed order of the same region.glog said:This equation cannot be integrated nicely, so I tried to reverse the order of integration:
\int^1_0 \int^1_x sin(x^2) dy dx