Question

can someone explain the solution for this?

2. Set up an iterated integral for S. 6zdV L" SLO པ་ཁ་ནི where is the region inside the cylinder x2 + y2 - 9 and between the planes 2 = 4 + and 2 = 10. Evaluate the innermost part of the integral only. Solution: In cylindrical coordinates we can write this as 6z dx dr de Jo Jetron) evaluating the inner integral gives 6" / 33 ir con() dr de - 6 1 1300 (300 - 3(4 + rs())) dr de 320

Answer 1

E NOW, Joe on the above yol qual More ihany I co-ordinates The given integral ise 6 z dv sh where is the legionJoside the way cylinder x² + y2 = 9 and between the and t = 10. plane ule have to evaluate the innere most part of integral only. cylindrical 4+ x the ma x= veces o = se sino and Then clearly the imit of z vaules varies from to Z Now, 2 We have 22+ y 2 (e.com ) + vecino) = vez ficas? + sino) = ve ² je, x2 + y² 2, the region inside The cylindre And, since is the x2 + y2 = 9 le x2+ 2 (3) 2 is clear that e varies Theis, it m o to 3 from

And. o vaules oço 21 from o to Je, thes, In cylindrical to cylindrical coordinates ordinates, the given Untegrald becomes a 67 dz de do a 4+ recoge Now, Rawaluating the innermost the poart Integral get 29 3 10 6. Z? u dr do 2 4+ ruoso 21 ,3 10 de do 4 + lecoso 2 3 [ too (10) 2 (4+4205 0 )') de de oo 3 [ 100-14.00)] de do 3 de do. 31 4+ le colo 308 b