devotion & mathematics

 Double Integrals : Integration over Rectangular Regions :                                                                           This page having some problems on Double Integrals followed by solutions.                                                                                                                         Back        1.   Evaluate ∬   xy (x 2 +y 2 )dx dy over [0,a;0,a]. SOLUTION :   2.       2 .  Evaluate   ...

 Repeated Integral   :                                  Let f(x) be a bounded function defined on the rectangle R=[a,b;c,d].            Suppose  ∫ f(x ,y) dy exists for each x  Ꜫ [a ,b] and y limits from c to d. If g(x) = ∫ f( x ,y )dy, y limits from c to d , then g(x) is a function on [a ,b] . If g(x) is also integrable on [a ,b] , then ∫g(x)dx =  ∫[  ∫ f(x , y)dy ] dx is called a repeated integral of f(x ,y) on R where x limits from a to b and y limits from c to d.                                                            Problems on Repeated Integrals : 1. Evaluate  ∫[  ∫ (x+y+1) dx ] dy and  ∫[ ∫(x+y+1) dy]dx , x limits from -1 to 1 and y limits are from -1 to 0. 2. Show tha...