Evaluate the integral cosh(r)dx dy dz Jo o Evaluate the integral cosh(r)dx dy dz Jo o
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
x=7 dy dz dx = x Z=0 The given triple integral sss =49-x² Y = 7-8 L dydzdx a) draw the region of integration for this double integral in the Zx plane 5*=7 62-4 dzdx z=0 b) Sketch the region corresponding to the triple integral SZ=49-x²
Evaluate the integral cosh(z2) dx dy dz J0 J0Jy
calculus 3 Tar LAami Jum er Z01J -z2 z sin x dy dz dx 1 8. Evaluate L Tar LAami Jum er Z01J -z2 z sin x dy dz dx 1 8. Evaluate L
Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded above by the cylinder z = 4 − x^2 below by the x, y-plane, and on the sides by the planes x =0, y = 2x and y = 4. Answer: ∫ (4, 0) ∫ (y/2, 0) ∫ (4−x^2, 0) 2xy dz dx dy = ∫ (2, 0) ∫ (4, 2x) ∫ (4−x^2, 0) 2xy dz dy dx = 128/3
must be in the order of dx dy dz 2. ONLY Find the limits when DV is written as dx dy dz (the integration has to be done in this order). SSS, f (x,y,z)dV where f(x, y, z) = 1 – x and D is the solid that lies in the first octant and below the plane 3x + 2y + z = 6.
(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)
The question is, evaluate the following integral. 1+x2+22 43. dy dx dz Jo Jo
(1 point) Evaluate the integral. 16 16- S. 1 (a2y2z2)1/2 dy dz dx 16-r 0 (1 point) Evaluate the integral. 16 16- S. 1 (a2y2z2)1/2 dy dz dx 16-r 0