MATH 201 Problems, Fall 2010

Integration Practice (Math 201 - Fall 2010) T. Tlas Question 1: Find the volume of the region in space bounded on the sides by y = x2, below by the plane z = 0 and above by the plane y + z = 1. Do the integration in all 6 orders dz dx dy , dx dy dz , etc . . . . Question 2: Find the integral of the function 1 � (x2 + y2)(x2 + y2 + z2) � � x2 + y2 � x2 + y2 + z2 + z � x2 + y2 + z2 � over the region in the first octant bounded below by the sphere x2 + y2 + (z − 1)2 = 1 and above by the cone x2 + y2 = (z − 2)2. Question 3: You are given that � 2 1 f(α) dα = 3. Find � 5 1 � 7 2 � exp (x+z2 exp (xz2))+2 exp (x+z2 exp (xz2))+1 f � y − exp (x + z2 exp (xz2)) � dy dx dz