Practice problems on double integrals

← Back to document page

Math 461Introduction to HildebrandPractice problems on double integralsThe problems below illustrate the kind of double integrals that frequently arise in probability first group of questions asks to set up a double integral of a general functionf(x,y) over a giving regionin thexy-plane. This means writing the integral as an iterated integral of the form f(x,y)dxdyand/or f(x,y)dydx, with specific limits in place of the asterisks. To do this, follow the steps above (mostimportantly, sketch the given region). The remaining questions are evaluations of integrals over Set up a double integral off(x,y) over the region given by 0<x<1,x<y<x+ : 1x=0 x+1y=xf(x,y)dydx2. Set up a double integral off(x,y) over the part of the unit square 0 x 1,0 y 1, on whichy : 1x=0 x/2y=0f(x,y)dydxor 1/2y=0 1x=2yf(x,y)dxdy3. Set up a double integral off(x,y) over the part of the unit square on whichx+y> : 1/2x=0 1y=1/2 xf(x,y)dydx+ 1x=1/2 1y=0f(x,y)dydx4. Set up a double integral off(x,y) over the part of the unit square on whichbothxandyare greaterthan : 1x=1/2 1y=1/2f(x,y)dydx5.

Practice problems on double integrals The problems below illustrate the kind of double integrals that frequently arise in probability applications. The first group of questions asks to set up a double integral of a general function f(x,y) over a giving region in the xy-plane. This means writing the integral as an iterated integral of the form ...

  Relating, Double, Of double, Double integrals