Evaluate the integral cosh(r)dx dy dz Jo o
Evaluate the integral cosh(r)dx dy dz Jo o
Do not evaluate, rewrite the integral using spherical coordinates 25-x² - y2 1 dz dx dy 05 NUS y=0 X-O Z=o
(1 point) Evaluate the integral by changing to cylindrical coordinates. 2 ,2 (a2 +y2)32 dz dy dz 2L,2
(1 point) Evaluate the integral by changing to cylindrical coordinates. 2 ,2 (a2 +y2)32 dz dy dz 2L,2
y2 + 4z2 = 16 Clearly construct a triple integral of the form dz dy dx to find the volume of the solid shown. The upper surface is defined by the cylinder y? +422 = 16. But do not evaluate the integral. 4 x
3. Consider the triple integral 2z sin(x2 + y2 +22 - 2x) dy da dz. Set up, but do not evaluate, an equivalent triple integral with the specified integration order. a) (6 pts) da dz dy b) (7 pts) dz dr de (Cylindrical Coordinates) c) (7 pts) dp do do (Spherical Coordinates)
Evaluate the integral cosh(z2) dx dy dz J0 J0Jy
2. Use cylindrical coordinates to solve the integral SSS (x2 + y2) dx dy dz D Z 2 Z = 2 z=Ż (x2 + y2) tor - y Х
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
2 147 a. Evaluate the triple integral (convert to oylindrical)12I, J xz dz dx dy b. Find the moment of inertia about the z-axis for the solid in the first octant bounded by x2+y2 -4 and z2-x2 + y2 if the density is given by: z. (Use cylindrical.) c. Find the mass of the solid bounded by z2 -x2 +y2 and z 1 in the first octant, if the density is given by: cos. (Use spherical.)
2 147 a. Evaluate...
25 2 6 Evaluate the integral S SS 3 cos (x2) -dx dy dz by changing the order of integration in an appropriate way. 417 o o Зу