4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y = 0 and x = T.

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

A:

Q: Y – 5x |dA 100 cos x + y

A: We have to evaluate the double integral ∬100cosy-5xx+ydxdy over the region D where the region D is a…

Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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: 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: 9. Compute the area of the region in the ry-plane wich is bounded by the x-axis and the curve r(t) =…

A: Introduction: To determine the parametric areas, one must compute the area under the mathbbR2R2…

Q: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: Evaluate the following integral: b.) !!!! xyz dv if S is the region bounded by the cylinders ² + y²…

A: According tot the given conditions the limi values of x,y and z are0≤x≤50≤y≤25-x20≤z≤25-x2Hence…

Q: 12) Find +he integral of the f(xiyia)=x+y? function on the region between the x4y1 and x?+y"= 9…

A: Convert the integral in cylindrical coordinate: ∭Vfx,y,zdxdydz=∫z=01∬1≤x2+y2≤9x2+y2dxdydz…

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

A:

Q: Use Green's Theorem to find the line integral. C is to be traversed in the counterclockwise…

A: In the question it is asked to calculate integral using Green's Theorem.

Q: Q.1B) Prove that: I = f, Cos () dxdy sin(1) %3D 2 where R the region bounded by x+y 1,x = 0,y = 0

A:

Q: 10. Use Green's Theorem to evaluate the line integral (e" - y) dx + x cos(y²) dy, where C is the…

A: 1/2 + ( (1/2 )sin 1)

Q: Use Green's Theorem to evaluate the line integral along the given positive (* 2x²y?) dy -4x хе dx +…

A:

Q: Calculate the iterated integral 5-x dx dy 2 х —1 and draw the region over which we are integrating.

A: To evaluate: ∫23dx∫x-15-x1ydy

Q: + y^5)dy] where C is the unit circle x^2 + y^2 = 1 traversed counterclockwise.

A: we have to compute the given integral ∮x5+y3dx-(x3+y5)dy     where C is unit circle x2+y2=1.C

Q: evaluate the double integral xy cos y dA over the given region R = [-1,1] × [0, 7 ]

A:

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

A:

Q: 6- Evaluate the line integral ScF · dr, where F = [xy, yz, xz] and C is the boundary of the…

A:

Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

A:

Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

A:

Q: 9. Compute the area of the region in the ry-plane wich is bounded by the z-axis and the curve r(t) =…

A:

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

A:

Q: Q.1B) Prove that: Iff, Cos) dxdy - = sin (1) where R the region bounded by x + y = 1, x = 0, y = 0

A: We use the change of variable to prive the given equality

Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

A:

Q: 4. Compute the integral x sin (xy) dA where R is the region 0 <x <1 and 0<y < .

A:

Q: 1) Evaluate the triple integral. | 6xy dV where E lies under the plane z = 1+x + y and above the…

A:

Q: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…

A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…

Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy = dA ду ax for the given path. C:…

A:

Q: Evaluate the triple integral ∭E(x+2y)dV where E is bounded by the parabolic cylinder y=2x2 and the…

A:

Q: 11. Let D be the triangular region bounded by the lines y = 1, y = 2x and y = -x. Evaluate the…

A: Given D be triangular region bounded by y=1,y=2x,y=-x.

Q: (b) ( y cos(ry) dA over the region R = {(x, y)|0<x < 1 and 1 < y <7/3}

A:

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: Compute the integral „2020 (5y + x*0 ") dx + (19x – e -e-4yCos(y) sin y) dy over the portion of the…

A:

Q: (2) Consider the region D in the ry-plane which is bounded by the following 2 4 curves y =, y = ỷ =…

A:

Q: 6- Evaluate the line integral fF dr, where F = [xy, yz, xz] and C is the boundary of the hemisphere…

A: the line integral f F dr, where F = [ry, yz, xz] and C is the boundary of the hemisphere x² + y² +…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

A: Solve

Q: Calculate the double integral: S,(y + xy – 2) dA where R= [0,2] x [1,2].

A:

Q: 1 Evaluate the double integral| dx dy where T is the quadrilateral bounded by the lines x = 1, x =…

A:

Q: 6. Evaluate the triple integral ry dV where E is bounded by the parabolic cylinders y = x² and r =…

A:

Q: Use Green's Theorem to evaluate the line integral √(x − x) dx + (2x - y) dy (y- for the given path.…

A:

Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

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

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

A:

Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

Q: 1 Integrate the function f (x, y) = over the region bounded by r-axis, line æ = 7, and the curve y =…

A:

Q: A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by…

A: Greens theorem

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.