My professor said " Hint: Use change of variables formula u= xy, v= x^2 - y^2" 31. Consider the triple integral II w 2x dv, where W is the solid three-dimensional region bounded by the surfaces z = x2 + y2, z = 2(x2 + y2), and z = 1. Express it as an iterated integral in cylindrical coordinates. Do not evaluate it.
1 Evaluate the triple integral SS Sw 2x dV, where w is the sulid in 3-dimensional region. bounded by the surfaces 2 = x²ty², 2=2 Cx² + y²), and 221
Please try helping with all three questions.......please 1 point) Integratef(x, y, z) 6xz over the region in the first octant (x,y, z 0) above the parabolic cylinder z = y2 and below the paraboloid Answer Find the volume of the solid in R3 bounded by y-x2 , x-уг, z-x + y + 24, and Z-0. Consider the triple integral fsPw xyz2 dV, where W is the region bounded by Write the triple integral as an iterated integral in the order...
6. Express the triple SSSE f(, y, z) dv erated integral in three different ways dzdxdy, dxdydz and dydzdx, where E is the solid bounded by the given surfaces (Don't evaluate the integral) x = 2, y = 2, z = 0, x + y – 2z = 2
please show all work 245 1) Sketch the region represented by 55 dydis on the attached grid. DA 2) SET UP the integral for both orders of integration of R: region bounded by y = x, y = 2x, x = 2 SS Vx++y* dxdy 3) Evaluate the following integral by converting to polar. 4) Use a double integral in polar to find the volume of the solid bounded by the equations z = x + y +1,2-0, x +...
6. (12pts) Consider the solid that is above the xy-plane, bounded above by =/4-x-y and below by +y a. Sketch the solid formed by the given surfaces b. Set up in rectangular coordinates the triple integral that represents the yolume of the solid. Sketch the appropriate projection. Do NOT evaluate the integrals. (Hint: Let dV- d dy de) c. Set up in cylindrical coordinates the triple integral that represents the volume of the solid. Sketch the appropriate projection. Do NOT...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
Solve: y" + 4y = 8 sin x. O y = A sin 2x + B cos 2x + (8/3) sin x O y = Ae^(2x) + Be^(-2x) y = A sin 2x + B cos 2x O y = A sin 2x + B cos 2x + sin x
3. (34 pts) This question has three parts (a), (b) ad e atd are (a) Evaluste the integralJ)codA, where w (b) Evaluate I (y+2)dV, where E is the solid in the first octant that lies under the paraboloid 4y (c) Find The volume of the solid bounded by the paraboloids : 3a + 4-r-r 3y2 and z 3. (34 pts) This question has three parts (a), (b) ad e atd are (a) Evaluste the integralJ)codA, where w (b) Evaluate I...
Please Answer the Following Questions (SHOW ALL WORK) 1. 2. 3. 4. Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...