how to change the order of a double integral (from dydx to dxdy)

[@Ninja20704]

Please do more calc 3 videos. That would be very much appreciated.

[@darcash1738]

y: [sqrtx, 1], x: [0, 1] Then flip the y, to get [1, sqrtx]. 1 is not in terms of x, so we just use the min of x, which is 0. And sqrtx = y --> x = y^2. Resulting in x: [0, y^2]. Plugging in the x vals, we can find the min and max. [sqrt(0), 1] --> y: [0, 1] x: [0, y^2], y: [0, 1] This is the technique i like to use, seems nice

[@darcash1738]

y: [tan^-1x, pi/6], x: [0, 1/sqrt3] x: [0, tan(y)], y: [0, pi/6]; where sin(0)/cos(0) = 0/1 = 0 and is the low bound for y

[@allmight801]

Changing order is easy for double integrals, for more challenge for double integrals do change of order while using polar coordinates drdphi and dphidr or change order of integration of triple integrals when you have cones planes and paraboloids intersecting each others

[@stephenbeck7222]

I think he has ones like that later in the series

[@GreenMeansGOF]

I needed this yesterday😅 I tried to create my own problem for my students so that they were forced to change the order but I failed. Neither order of integration was solvable.

[@bprpcalculusbasics]

😆