Section You should be able to … Example Review Exercises
14.1 1 Find Riemann sums of \(z=f(x, y)\) over a closed rectangular region (p.904) 1 7(a), 7(b)
2 Find the value of a double integral defined on a closed rectangular region (p. 906) 2, 3, 4 1, 2, 7(c), 8, 9
3 Find the volume under a surface and over a rectangular region (p. 908) 5 10, 11
14.2 1 Use Fubini’s Theorem for an \(x\)-simple region (p. 914) 1 3–6, 13
2 Use Fubini’s Theorem for a \(y\)-simple region (p. 916) 2, 3 3–6, 13, 14, 54
3 Work with properties of double integrals (p. 917) 4, 5 12
4 Use double integrals to find area and volume (p. 918) 6, 7, 8 15–18, 20
14.3 1 Find a double integral using polar coordinates (p. 924) 1, 2, 3 19, 52
2 Find area and volume using polar coordinates (p. 925) 4, 5, 6 21, 22
14.4 1 Find the mass and center of mass of a lamina (p. 929) 1, 2 23–25
2 Find moments of inertia (p. 933) 3 26
14.5 1 Find the surface area that lies above a region \(R\) (p. 938) 1, 2, 3 27–29
14.6 1 Find a triple integral defined over a closed box (p. 942) 1 30
2 Find a triple integral defined over a more general solid (p. 942) 2 31, 32
3 Find the volume of a solid (p. 944) 3 15–17, 35, 36
4 Find the mass, center of mass, and moments of inertia of a solid (p. 944) 4, 5 62
5 Find a triple integral defined over \(xz\)-simple and \(yz\)-simple solids (p. 946) 6 33
14.7 1 Convert rectangular coordinates to cylindrical coordinates (p. 950) 1 37(a)–40(a)
2 Find a triple integral using cylindrical coordinates (p. 951) 2, 3, 4, 5 43–45, 47–51, 53
14.8 1 Convert rectangular coordinates to spherical coordinates (p. 956) 1, 2 37(b)–40(b)
2 Find a triple integral using spherical coordinates (p. 958) 3, 4, 5, 6 34, 41, 42, 46–51
14.9 1 Find a Jacobian in two variables (p. 963) 1 55, 56
2 Change the variables of a double integral using a Jacobian (p. 964) 2, 3 58–60
3 Change the variables of a triple integral using a Jacobian (p. 965) 4 57, 61