1 Limits And Continuity 2 The Derivative 3 Topics In Differentiation 4 The Derivative In Graphing And Applications 5 Integration 6 Applications Of The Definite Integral In Geometry, Science, And Engineering 7 Principles Of Integral Evaluation 8 Mathematical Modeling With Differential Equations 9 Infinite Series 10 Parametric And Polar Curves; Conic Sections 11 Three-dimensional Space; Vectors 12 Vector-valued Functions 13 Partial Derivatives 14 Multiple Integrals 15 Topics In Vector Calculus expand_more
14.1 Double Integrals 14.2 Double Integrals Over Nonrectangular Regions 14.3 Double Integrals In Polar Coordinates 14.4 Surface Area; Parametric Surfaces 14.5 Triple Integrals 14.6 Triple Integrals In Cylindrical And Spherical Coordinates 14.7 Change Of Variables In Multiple Integrals; Jacobians 14.8 Centers Of Gravity Using Multiple Integrals Chapter Questions expand_more
Problem 1QCE: The total mass of a lamina with continuous density function x,y that occupies a region R in the... Problem 2QCE: Consider a lamina with mass M and continuous density function x,y that occupies a region R in the... Problem 3QCE: Let R be the region between the graphs of y=x2andy=2xfor0x1. The area of R is 76 and the centroid of... Problem 1ES: Find the mass and center of gravity of the lamina. A lamina with density x,y=x+y is bounded by the... Problem 2ES: Find the mass and center of gravity of the lamina. A lamina with density x,y=y is bounded by... Problem 3ES: Find the mass and center of gravity of the lamina. A lamina with density x,y=xy is in the first... Problem 4ES Problem 5ES: For the given density function, make a conjecture about the coordinates of the center of gravity and... Problem 6ES Problem 7ES: Make a conjecture about the coordinates of the centroid of the region and confirm your conjecture by... Problem 8ES: Make a conjecture about the coordinates of the centroid of the region and confirm your conjecture by... Problem 9ES Problem 10ES Problem 11ES Problem 12ES Problem 13ES: Show that in polar coordinates the formulas for the centroid x,y of a region R are... Problem 14ES: Use the result of Exercise 13 to find the centroid x,y of the region. The region enclosed by the... Problem 15ES Problem 16ES: Use the result of Exercise 13 to find the centroid x,y of the region. The region above the x-axis... Problem 17ES Problem 18ES Problem 19ES: Find the centroid of the solid. The tetrahedron in the first octant enclosed by the coordinate... Problem 20ES Problem 21ES: Find the centroid of the solid. The solid bounded by the surface z=y2 and the planes x=0,x=1,andz=1. Problem 22ES Problem 23ES: Find the centroid of the solid. The solid in the first octant that is bounded by the sphere... Problem 24ES: Find the centroid of the solid. The solid enclosed by the xy-plane and the hemisphere z=a2x2y2. Problem 25ES: Find the mass and center of gravity of the solid. The cube that has density x,y,z=ax and is defined... Problem 26ES Problem 27ES: Find the mass and center of gravity of the solid. The solid that has density x,y,z=yz and is... Problem 28ES: Find the mass and center of gravity of the solid. The solid that has density x,y,z=xz and is... Problem 29ES: Find the center of gravity of the square lamina with vertices 0,0,1,0,0,1,and1,1 if (a) the density... Problem 30ES: Find the center of gravity of the cube that is determined by the inequalities 0x1,0y1,0z1 if (a) the... Problem 31ES: Use the numerical triple integral capability of a CAS approximate the location of the centroid of... Problem 32ES: The accompanying figure on the next page shows the solid that is bounded above by the surface... Problem 33ES: Use cylindrical coordinates. Find the mass of the solid with density x,y,z=3z that is bounded by the... Problem 34ES: Use cylindrical coordinates. Find the mass of a right circular cylinder of radius a and height h if... Problem 35ES: Use spherical coordinates. Find the mass of a spherical solid of radius a if the density is... Problem 36ES Problem 37ES: Use cylindrical coordinates to find the centroid of the solid. The solid that is bounded above by... Problem 38ES: Use cylindrical coordinates to find the centroid of the solid. The solid that is bounded by the cone... Problem 39ES: Use the Wallis sine and cosine formulas:... Problem 40ES: Use the Wallis sine and cosine formulas:... Problem 41ES: Use spherical coordinates to find the centroid of the solid. The solid in the first octant bounded... Problem 42ES: Use spherical coordinates to find the centroid of the solid. The solid bounded above by the sphere... Problem 43ES: Find the mass of the solid that is enclosed by the sphere x2+y2+z2=1 and lies above the cone z=x2+y2... Problem 44ES: Find the center of gravity of the solid bounded by the paraboloid z=1x2y2 and the xy-plane, assuming... Problem 45ES: Find the center of gravity of the solid that is bounded by the cylinder x2+y2=1, the cone z=x2+y2,... Problem 46ES: Find the center of gravity of the solid hemisphere bounded by z=a2x2y2 and z=0 if the density is... Problem 47ES: Find the centroid of the solid that is enclosed by the hemispheres y=9x2z2,y=4x2z2 and the plane... Problem 48ES: Suppose that the density at a point in a gaseous spherical star is modeled by the formula =0e/R3... Problem 49ES: The tendency of a lamina to resist a change in rotational motion about an axis is measured by its... Problem 50ES: The tendency of a lamina to resist a change in rotational motion about an axis is measured by its... Problem 51ES: The tendency of a solid to resist a change rotational motion about an axis is measured by its moment... Problem 52ES: The tendency of a solid to resist a change rotational motion about an axis is measured by its moment... Problem 53ES: The tendency of a solid to resist a change rotational motion about an axis is measured by its moment... Problem 54ES: The tendency of a solid to resist a change rotational motion about an axis is measured by its moment... Problem 55ES: These exercises reference the Theorem of Pappus: If R is a bounded plane region and L is a line that... Problem 56ES: These exercises reference the Theorem of Pappus: If R is a bounded plane region and L is a line that... Problem 57ES: These exercises reference the Theorem of Pappus: If R is a bounded plane region and L is a line that... Problem 58ES: These exercises reference the Theorem of Pappus: If R is a bounded plane region and L is a line that... Problem 59ES: These exercises reference the Theorem of Pappus: If R is a bounded plane region and L is a line that... Problem 60ES: It can be proved that if a bounded plane region slides along a helix in such a way that the region... Problem 61ES format_list_bulleted