Problem 1RE: Evaluating an Integral In Exercises 1 and 2, evaluate the integral. 03xsin(xy)dy Problem 2RE Problem 3RE: Evaluating an Integral In Exercises 3 - 6, evaluate the integral. 0101+x(3x+2y)dydx Problem 4RE Problem 5RE Problem 6RE Problem 7RE Problem 8RE Problem 9RE Problem 10RE Problem 11RE Problem 12RE Problem 13RE: Changing the Order of Integration In Exercises 11-14, sketch the region K whose area is given by the... Problem 14RE Problem 15RE Problem 16RE Problem 17RE Problem 18RE Problem 19RE Problem 20RE: Finding Volume In Exercises 17-20, use a double integral to find the volume of the indicated solid. Problem 21RE Problem 22RE Problem 23RE Problem 24RE Problem 25RE Problem 26RE Problem 27RE Problem 28RE Problem 29RE Problem 30RE Problem 31RE: AreaIn Exercises 31 and 32, sketch a graph of the region bounded by the graphs of the equations.... Problem 32RE Problem 33RE Problem 34RE: Converting to Polar Coordinates Write the sum of the two iterated integrals as a single iterated... Problem 35RE Problem 36RE Problem 37RE Problem 38RE: Finding the Center of Mass In Exercises 37-40, Find the mass and center of mass of the lamina... Problem 39RE Problem 40RE Problem 41RE Problem 42RE: Finding Moments of Inertia and Radii of GyrationIn Exercises 41 and 42, find Ix,Iy,I0,x, and y for... Problem 43RE: Finding Surface AreaIn Exercises 4346, find the area of the surface given by z=f(x,y) that lies... Problem 44RE: Finding Surface AreaIn Exercises 4346, find the area of the surface given by z=f(x,y) that lies... Problem 45RE Problem 46RE: Finding Surface AreaIn Exercises 4346, find the area of the surface given by z=f(x,y) that lies... Problem 47RE Problem 48RE Problem 49RE Problem 50RE Problem 51RE Problem 52RE Problem 53RE Problem 54RE Problem 55RE Problem 56RE Problem 57RE: Changing the Order of Integration In Exercises 57 and 58, sketch the solid whose volume is given by... Problem 59RE Problem 60RE: Center of Mass In Exercises 59 and 60, find the mass and the indicated coordinate of the center of... Problem 61RE Problem 62RE Problem 63RE Problem 64RE Problem 65RE Problem 66RE Problem 67RE: VolumeIn Exercises 67 and 68, use cylindrical coordinates to find the volume of the solid. Solid... Problem 68RE Problem 69RE Problem 70RE Problem 71RE Problem 72RE Problem 73RE: Finding a JcobianIn Exercises 7174, find the Jacobian (x,y)/(u,v) for the indicated change of... Problem 74RE Problem 75RE Problem 76RE: Evaluating a Double Integral Using a Change of VariablesIn Exercises 7578, use the indicated change... Problem 77RE Problem 78RE Problem 1PS: VolumeFind the volume of the solid of intersection of the three cylinders x2+z2=1,y2+z2=1, and... Problem 2PS: Surface AreaLet a,b,c, and d be positive real numbers. The portion of the plane ax+by+cz=d in the... Problem 3PS: Using a Change of variables The figure shows the region R bounded by the curves... Problem 4PS: ProofProve that limn0101xnyndxdy=0. Problem 5PS: Deriving a Sum Derive Eulers famous result that was mentioned in Section 9.3, n=11n2=26 by... Problem 6PS: Evaluating a Double IntegralEvaluate the integral 001(1+x2+y2)2dxdy. Problem 7PS: Evaluating Double IntegralsEvaluate the integrals 0101xy(x+y)3dxdyand0101xy(x+y)3dydx. Are the... Problem 8PS: VolumeShow that the volume of a spherical block can be approximated by Vp2sinp. (Hint: See Section... Problem 9PS: Evaluating an IntegralIn Exercises 9 and 10, evaluate the integral. (Hint: See Exercise 63 in... Problem 10PS Problem 11PS Problem 12PS Problem 14PS Problem 15PS Problem 16PS: SprinklerConsider a circular lawn with a radius of 10 feet, as shown in the figure. Assume that a... Problem 18PS: Volume The figure shows a solid bounded below by the plane z=2 and above by the sphere x2+y2+z2=8.... format_list_bulleted