31. Compute (x + 3y)dx dy, where D is the shaded region in Figure 16. Hint: Use the map G(u, v) = (u – 2v, v). %3D x+ 2y = 10 3 1 6. x+ 2y = 6 10 FIGURE 16 len

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: Find the value of p(x), q(x) and r(x) in the Sturm-Liouville Boundary Value problem dy dy A +3x dx…

A: Sturm-Leouville Boundary value problem: Sturm-Leouville Boundary value problem is a differential…

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

A:

Q: S.(2x° +5y )dx+(2x-4y') dy C:boundary of the region lying between the graphs of x² +y² = 16 and x +y…

A:

Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

A:

Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

A:

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

Q: 1. Compute  E yz dV , where E is the region above z  0, below z  y, and inside x 2 y 2  4

A: Obtain the limit of integration as follows.

Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2,x = 1,Ax = 0.5 a. Ay = 1.25, dy = 1…

A:

Q: Volumes of solids Find the volume of the following solids.

A: The region is bounded by the curves, The region is shown in the graph given below,

Q: (b) y T= x (p) 3. Region bounded by: y = 4 – x² and y = 0. Rotate about: (a) the x-axis (с) у — —1

A: I have solved the first part for next parts repost the question

Q: The numerical value of 34 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

A:

Q: 3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) =…

A:

Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Compute (1) (ii) the marginal p.m.f. of X. P(Y=-1|X=1).

A:

Q: 3) The circulation of W = p coso ao + z sino az around closed path L shown in figure, is: a) v3 - 2…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find general polutien yoy! + x = 0 of followoing eeparable obts. ODES. a. y' = e*** yz 2メー1 b. = e²

A:

Q: 1. Evaluate , 3y e ²x dA where D is the region bounded by x = ₁x = 1, y = 1 and y = 2. 2

A:

Q: a) Evaluate ff, (3 – 4x)dV where E is the region below z = 4 – xy and above the region in xy – plane…

A: To evaluate the given triple integral.

Q: (1. 1. 1) Evaluate the integral (5xy + 22°) dx + 5xf dy + (12z + 1) dz. (0.0.0) (Hint. Try the path…

A:

Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: When the group of terms in a first-order DE contains y dx - x dy , the following integrating factors…

A: For the given statement

Q: (d) Compute the marginal pmf of X. 0 Px(x) Compute the marginal pmf of Y. y Py(y) 0 1 1 Using px(x),…

A:

Q: 3.33 Let D = 2pz'a, + p cos´ þa,. Evaluate (a) $D· dS (b) J,V· Ddv over the region defined by 2 < p<…

A: Given: Let D=2ρz2aρ+ρcos2ϕaz a∮SD.dS Here, We know that surface vector dS is defined as…

Q: 4. Evaluate fl, cos (2) dA where D is the region bounded by D = {(x, y)/ vLT <x < V3Ln,0 <y< x² }.

A:

Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: 15. Evaluate the line integral J. (3xy* - 6xy ]dx + (4x'y - 3x) dy, where C is any path from (1, 2)…

A:

Q: dz Let z=e"In(xy), determine dx et (1+xin(xy)) dz A %3D дх az (1+xyln(xy)) %3D дх y (1+yln(xy)) %3D…

A: Explanation of the answer is as follows

Q: 19 9% Set up the iterated double integral S S dy dæ as dxdy such that: 0 0 i. the limits of x ii.…

A:

Q: In 2 If we reverse the order of integration o f(c, y)dy da, then we obtain: Select one: O a So f(x,…

A: This question is related to Integral calculus

Q: The shaded area shown in (Figure 1) is bounded by y axis and the curve y? = (1.44 – x) m, where z is…

A:

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

A:

Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

A:

Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

A:

Q: 11 ComputePydz - zy'dy, nhere Dis descnbed by z² + y²s1. -1/2

A: Given an integral : ∫∂D x2y dx - xy2 dy  where D is : x2+y2≤1 We need to compute the integral.

Q: : 0s 0s n, Os zs 1, 6Vzs rs 6}. Let E= Compute y?e(x2+y?)³ dv•

A: Given that, Let E=r,θ,z : 0≤θ≤π, 0≤z≤1, 6z≤r≤6 compute ∬∫Ey2ex2+y22dV

Q: 4. 3x? ey dx + e dy C C: boundary of the region lying between the squares with vertices (1, 1), (-1,…

A:

Q: 4. Aşağıdaki denklemi y(2)=1 başlangıç koşulu için çözünüz dy (x² + 1 ) + 4xy = x dx

A:

Q: Evaluate 7x dV where E is the region that lies inside the cylinder x2 + y² = 8 E and between the…

A:

Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

A:

Q: dy _Зy +x dx Зx + у

A:

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

A:

Q: Compute the flux

A: by divergence theorem flux=∫∫sF.ds   =∫∫∫E div F dv Given F=x,y,zand   S; is the boundary of the…

Q: Consider theD. E. M(x, y)dx + N(x, y)dy = 0 if M - N = 24M, M,N, = 1 and M = 2 – N? then %3D %3D %3D…

A:

Q: Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following…

A: To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are…

Q: The equation (4x-2y+5)dx +(2y²-2x)dy =0 is a lan A Bernoulli's DE B Exact DE C) LDE of order 1 D)…

A:

Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

A:

Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

A: