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23 y?z? sin(x4) dx dy dz
LL L'Amazz de de dy= L*IL 4az dz dx dy = Edz dr de y Jv+y MMMMMM 0 = 02 = Evaluate the integral 4xz dz da dy =
8. Clearly construct a triple integral of the form dz dy dr to find the volume of the solid shown. The solid is constructed by taking the paraboloid :=x2 + y and have the top cut by the plane z=4y. But do not evaluate the integral. 1 10 8 ry
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
scan it clear please 6. (15points ) Evaluate the triple integral cln(y+1) е-2" dr dy dz. С""""
Help me answer, thank you! Find dy for the following equation. y=3x19-x4 dy= dx
Q3. Sketch the region of integration for the integral [5(8,19,2) dr dz dy. (2, y, z) do dzdy. Write the five other iterated integrals that are equal to the given iterated integral. Q4. Use cylindrical coordinates and integration (where appropriate) to complete the following prob- lems. You must show the work needed to set up the integral: sketch the regions, give projections, etc. Simply writing out the iterated integrals will result in no credit. frs:52 (a) Sketch the solid given...
sin (z) cos3 (z) dz. y° cos (3y) dy. sin (z) cos3 (z) dz. y° cos (3y) dy.
Question 15 Convert the triple integr V yzé dz dy dr to cylindrical coordinates. © SE S SA--> »?z? sin º dz dr de So So S4_»(4 – „2)2 sin 0 dz dr de SL S4rz2 sin 0 dz dr de p2z2 sin dz dr do LT S Sone p222 sin 0 dz dr de
Suppose that x4 + y4 = 82. (1) Use the method of implicit differentiation to find dy Preview (2) Find the equation of the tangent line at the point (x, y) = (-1, -3). The equation is y = Preview