4. Given it the integral 132-8272 CVT-xa AL z dzdy dx Vx?tyz 0 - 116=x2 b)...
4. Given the integral 32-12 72 (4 1/16x² /132-x² - y2 z dzdy dx - 116xz xyz a) Rewrite it in cylindrical coordinates b) Rewrite it in 'spherical wordinates c) Evaluate it using whichever coordinates you prefer.
Use a change of variables to evaluate the following indefinite integral. ( (Vx+5) 4 3 dx J2V Determine a change of variables from x to u. Choose the correct answer below. OA. u= (x + 5)^ OB. u= VX +5 OC. Uz OD. u= Write the integral in terms of u. (Vx+5) dx = du 28x Evaluate the integral (Vx+5)* dx=0 2/8 Click to select your answer(s).
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...
Evaluate the integral using the given substitution. OA. $x*(88 - 4) *dx, u=x2-4 35x25 - 4+0 O B. 15 (85 - 4) + 12 / 3 (x3 - 4) + OD. 13 (x² - 4) + c +C Oc. +C
(2) Let F zi + xj+yk and consider the integral vx Fi n dS where S is the surface of the paraboloid z = 1-x2-y2 corresponding to 0, and n is a unit normal vector to S in the positive z-direction. (a) Apply Stokes' theorem to evaluate the integral. b) Evaluate the integral directly over the surface S. (c) Evaluate the integral directly over the new surface S which is given by the disk
(2) Let F zi + xj+yk...
C V I return K shift M 9e ation 14. Consider the triple integral dzdx dy representing a solid S. Let R be the projection of S onto the plane z=0. (a) Draw the region R. (b) Rewrite this integral SSls dzdy dx. as 15. Consider the transformation T: x = 2u + v, y = u + 20. (a) Describe the image S under T of the unit square R = {(u, u) | 0 using a change of...
The figure shows the region of integration for the integral. fx, y, z dy dz dx 0 Jo Rewrite this integral as an equivalent iterated integral in the five other orders. (Assume yx) 6x and z(x)-36-) x. f(x, y, 2) dy dx dz x, , z) dz dx dy f(x, y, z) dz dy dx f(x, y, z) dx dy dz fx, y, z) dx dy dz J0 Jo Jo f(x, y, z) dz dx dy 0 0 f(x, y,...
4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component.
4. Evaluate the Surface Integral [f(r,y,0)nds , where S is the part of the surface z-Vx+y* below z-1, and i is the unit outer normal to S with negative z- component.
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
Please show al work
1. (6pts) Given ( f(z)dx = 31 and ( f(z)dx = -11, evaluate using properties of definite integrals: a) ['f(z)dx = b) [ f()dx = c) ["-2f(x)dx =