evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C is the ellipse 4x² + y² = 4

Q: 2. Give iterated integrals for (xz*)dS where S is the part of the cylinder x² + y = 9 above the…

A: Given that x2+y2=9 and the part of the cylinder which is above XY plane implying that z > 0. We…

Q: Evaluate the double integral. (2х + у) dA, D = {(x, y) | 1<ys 4, y – 3 <x< 3}

A:

Q: Calculate the double integral || x + y)?e -r dx dy where R is the square with vertices (4, 0), (0,…

A: Given: ∫∫Rx+y2ex2-y2 dx dy where R is the square with vertices 4,0, 0,4, -4,0, 0,-4

Q: Q.3 Find the double integral for L. x² dydx, where R between y = 1/x , y = x and x = 2 SR

A: From the given region, y varies from y = x  to y = 1/x and x varies from x = 1 to x = 2. The…

Q: 15. Evaluate the double integral (a + 6y? + bx²y) dA, where R = {(x, y) E R² : |x| + \y| < 1}.

A:

Q: Evaluate the iterated integral. 2y (2 + 4x² + 8y²) dx dy 0 Jy

A: To evaluate:∫02∫y2y2+4x2+8y2dxdy

Q: Calculate the double integral || (x + y)?ex -ý dx dy where R is the square with vertices (2, 0), (0,…

A:

Q: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

A: Given line integral is ∮Cex+y2dx+ey+x2dy, where C is the boundary of the region between the parabola…

Q: Evaluate the line integral [21r²yzds with respect to s along the 2 curve C : x = t₁ y = t², z =…

A:

Q: Evaluate the iterated integral. m/2 (y/6 1/y sin y dz dx dy

A: We will evaluate the given integral.Below find the detailed solution in the image.

Q: (9) Evaluate // 2² + y² + z²)³/? dV where D is the solid region in the first octant between the two…

A: Volume between the two spheres using spherical coordinates

Q: Evaluate the line integral by the two following methods. xy dx + x?y3 dy Cis counterclockwise around…

A:

Q: 4. Evaluate the integral f. x'y°dy – x°y'dx, where C is the square determined by the lines x = 0, y…

A: As per Bartleby's answering policy, we can answer only one question and here we have answered the…

Q: #6. Evaluate the line integral (y dx +z dy +x dz), where C is given by x = Vt, y = t, z = t? with…

A:

Q: #1. Evaluate the iterated integrals (a) || (6x?y+4x - y) dx dy -2 (b) y2 x²y dxdy

A:

Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 <ys 2, y – 1 < x< 1}

A:

Q: Evaluate the line integral by following the given steps. 4xy dx + 2x²y dy C is the triangle with…

A:

Q: V3y x²+y? 1. Evaluate the integral S S. S*" , dx dy dz.

A: Given:∫12∫z2∫03yyx2+y2dxdydz∫yx2+y2dxsubstitute u =xy→dudx=1y→dx=ydu=∫y2y2u2+y2du=∫1u2+1duThis is…

Q: Evaluate the double integral. 7y2 dA, D = {(x, y) I –1<y<1, -y – 2< x< y}

A: Explanation of the answer is as follows

Q: Eval u ate the double integrals overs the indicated re sions り ye JA, R: the region bonnded by the…

A:

Q: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: 3. Evalnate. the. fallowing.denble.integrals..by.convecking.bo. Can polar.Caa.r.dinates. ... 2 2…

A:

Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = E : 6y² + 6z²…

A:

Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy

A:

Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

A:

Q: 5. Evaluate the double integral (a + 3x + bry) dA, where R= {(x, y) E R² : |x|+ |y| 0 and b > 0).

A: To Evaluate: ∬Ra+3x2+bxydA, whereR=x,y∈ℝ2:x+y≤1

Q: 4. the value of the given integrals | z - i | = 2,(z € C) around the circle compute for positive…

A:

Q: Find the value of the double integrals for: Ql: f(x, y) - ycos xy over the rectangle 0 sxS T, 0 sys1

A:

Q: 3) S. (3x? – 3yz + 2xz)dx + (3y? – 3xz + z²)dy + (3z2 - 3xy + x2 + 2yz)dz Calculate the curvilinear…

A:

Q: Q.3 Find the double integral for L. x? dydx, where R between y = 1/x ,y= x and x = 2

A: From the given problem:   I=∫∫Rx2dydx   And curves are: y=1x; y=x and x=2   So the bounded region is…

Q: 5) Evaluate the line integral S YX²dX + XY²dY on curve C, where C is the upper portion of the www m…

A:

Q: 3 The integral ³³ g(x, y) dxdy is equivalent 3 to ₁ ³x g(x, y) dydx

A:

Q: 9-x2 C: Change to polar and evaluate the double integrals S (x3 + xy?)dydx V9-x2

A:

Q: Evaluate the integral S (10 – 2z) dS, where S is the part of the surface z = S inside the cylinder…

A: The given surfaces are:z=5-x22-y22and the cylinder is x2+y2=1.This can be plotted as follows.

Q: y? = 1? Which of the following integrals represents the length of the upper half of the ellipse 25…

A: Topic = Application of integration  Correct answer = A

Q: Q#4. Is Green's theorem applicable for all types of line integrals? Explain clearly. Use Green's…

A:

Q: 6. Use Green's Theorem to evaluate the line integral fc 2xy dx + (x² + y²) dy, if C is the ellipse…

A: Let R be simply connected region with a piecewise  smooth boundary  'C'. If functions 'M' and 'N'…

Q: Evaluate the iterated integral. ||| x*y² + z² dx dy dz 0.

A:

Q: Which of the following integrals gives the area of the surface obtained by 3 rotating the curve y…

A: Solution: The objective is to determine which of the following integrals gives the area of the…

Q: late the double integral. (6z²y – 5y*) dA, R= {(z,y) | 0< z S 3,0 syS1}

A: Given: The double integral ∫∫R6x2y3-5y4dA,       R=x, y| 0≤x≤3, 0≤y≤1. Here, y varies from 0 to 1…

Q: 14. Find the line integral of f(x, y, z) = V3/(x² + y² + z?) over the curve r(t) = ti + tj + tk, 1 <…

A:

Q: Find the iterated integral 1∫0y2∫y(x+2y)dxdy.

A: We have given a double integral;

Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

A:

Q: Use Green's Theorem to evaluate the line integral , 6y² dx + 5x² dy, where Cis the boundary of the…

A: Green's Theorem: ∮C(Pdx+Qdy)=∫∫R∂Q∂x-∂P∂ydA

Q: Q.01: Use Green's theorem to evaluate the line integral £ e2*sin2ydx + (e²*cos2y)dy, where C is the…

A:

Q: Calculate the double integral || (x + y)?e* - Ý dx dy where R is the square with vertices (2, 0),…

A: According to the given information, it is required to find the integral over R where R is square.

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…

Q: Evaluate the iterated integral. V 4 - y2 (x + y) dx dy

A: