 5.1: Z 2 sin cos d = sin2 or cos2 or 1 2 cos 2. Hint: Use trig identities
 5.2: Z dx x2 + a2 = sinh1 x a or ln x + px2 + a2 . Hint: To find the sin...
 5.3: Z dy py2 a2 = cosh1 y a or ln y + py2 a2 . Hint: See hints.
 5.4: Z p1 + a2x2 dx = x 2 p1 + a2x2 + 1 2a sinh1 ax or x 2 p1 + a2x2 + 1...
 5.5: Z K dr 1 K2r2 = sin1 Kr or cos1 Kr or tan1 Kr 1 K2r2 .
 5.6: Z K dr r r2 K2 = cos1 K r or sec1 r K or sin1 K r or tan1 K r2 K2 .
 5.7: RR A(2x 3y) dx dy, where A is the triangle with vertices (0, 0), (2...
 5.8: RR A 6y2 cos x dx dy, where A is the area inclosed by the curves y ...
 5.9: RR A sin x dx dy where A is the area shown in Figure 2.8.
 5.10: RR A y dx dy where A is the area in Figure 2.8.
 5.11: RR A x dx dy, where A is the area between the parabola y = x2 and t...
 5.12: RR y dx dy over the triangle with vertices (1, 0), (0, 2), and (2, 0).
 5.13: RR 2xy dx dy over the triangle with vertices (0, 0), (2, 1), (3, 0).
 5.14: RR x2ex2y dx dy over the area bounded by y = x1, y = x2, and x = ln 4.
 5.15: RR dx dy over the area bounded by y = ln x, y = e + 1 x, and the x ...
 5.16: RR (9 + 2y2) 1 dx dy over the quadrilateral with vertices (1, 3), (...
 5.17: RR (x/y) dx dy over the triangle with vertices (0, 0), (1, 1), (1, 2).
 5.18: RR y1/2 dx dy over the area bounded by y = x2, x + y = 2, and the y...
 5.19: Above the square with vertices at (0, 0), (2, 0), (0, 2), and (2, 2...
 5.20: Above the rectangle with vertices (0, 0), (0, 1), (2, 0), and (2, 1...
 5.21: Above the triangle with vertices (0, 0), (2, 0), and (2, 1), and be...
 5.22: Above the triangle with vertices (0, 2), (1, 1), and (2, 2), and un...
 5.23: Under the surface z = y(x + 2), and over the area bounded by x + y ...
 5.24: Under the surface z = 1/(y+2), and over the area bounded by y = x a...
 5.25: Z 1 x=0 Z 33x y=0 dy dx
 5.26: Z 2 y=0 Z 1 x=y/2 (x + y) dx dy
 5.27: Z 4 x=0 Z x y=0 y x dy dx
 5.28: 1 y=0 Z 1y2 x=0 y dx dy
 5.29: Z y=0 Z x=y sin x x dx dy
 5.30: 2 x=0 Z 2 y=x ey2/2 dy dx
 5.31: Z ln 16 x=0 Z 4 y=ex/2 dy dx ln y
 5.32: Z 1 y=0 Z 1 x=y2 ex x dx dy
 5.33: A lamina covering the quarter disk x2 + y2 4, x > 0, y > 0, has (ar...
 5.34: A dielectric lamina with charge density proportional to y covers th...
 5.35: A triangular lamina is bounded by the coordinate axes and the line ...
 5.36: A partially silvered mirror covers the square area with vertices at...
 5.37: Z 2 x=1 Z 2x y=x Z yx z=0 dz dy dx
 5.38: Z 2 z=0 Z 2 x=z Z z y=8x dy dx dz
 5.39: Z 3 y=2 Z 2 z=1 Z 2y+z x=y+z 6y dx dz dy
 5.40: Z 2 x=1 Z 2x z=x Z 1/z y=0 z dy dz dx.
 5.41: Find the volume between the planes z = 2x + 3y + 6 and z = 2x + 7y ...
 5.42: Find the volume between the planes z = 2x + 3y + 6 and z = 2x + 7y ...
 5.43: Find the volume between the surfaces z = 2x2 + y2 + 12 and z = x2 +...
 5.44: Find the mass of the solid in if the density is proportional to y.
 5.45: Find the mass of the solid in if the density is proportional to x.
 5.46: Find the mass of a cube of side 2 if the density is proportional to...
 5.47: Find the volume in the first octant bounded by the coordinate plane...
 5.48: Find the volume in the first octant bounded by the cone z2 = x2 y2 ...
 5.49: Find the volume in the first octant bounded by the paraboloid z = 1...
 5.50: Find the mass of the solid in if the density is z.
Solutions for Chapter 5: Multiple Integrals; Applications of Integration
Full solutions for Mathematical Methods in the Physical Sciences  3rd Edition
ISBN: 9780471198260
Solutions for Chapter 5: Multiple Integrals; Applications of Integration
Get Full SolutionsSince 50 problems in chapter 5: Multiple Integrals; Applications of Integration have been answered, more than 16770 students have viewed full stepbystep solutions from this chapter. Chapter 5: Multiple Integrals; Applications of Integration includes 50 full stepbystep solutions. Mathematical Methods in the Physical Sciences was written by and is associated to the ISBN: 9780471198260. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Mathematical Methods in the Physical Sciences, edition: 3.

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