5. D is the region in the xy-plane bounded by the curves x = cos(y), 3y 27Tx, Зу 3 — 2тх. Evaluate x dA.

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

A:

Q: 12. In the xy plane the region D is bounded by the lines y = 2x + 6 y = 2r +1, y = -3r +6, and y =…

A: Given: y=2x+6 y=2x+1 y=-3x+6 y=-3x+1

Q: The area of the region bounded by the curves 2y2 +2 and z 2y+2 is 2. 3 5 -1 -2 16 17 (A) 3 (B) 3 13…

A:

Q: A region R is bounded by the graphs of  y=0.8 (x)^1/2 and y=0.8x.  Find the moments Mx and My of R…

A: Given,

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

A: Solution :-

Q: d the volume V of the solid obtained by rotating the region bounded by the ren curves about the…

A:

Q: Sketch the region enclosed by the given curves. y = 3 cos(5x), y= 3 – 3 cos(5x), 0 < x< 1/5 y y 6- 2…

A:

Q: The area bounded by the curve z 4y+7, the y-ax y =0 and y 2 is dy3D O 18 22 11 O 15

A: Area bounded by the curve can be calculated as

Q: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

A:

Q: Use Green’s Theorem to evaluate  ∫ sin 5y dx + 5x dy  around the boundary curve C of the region R,…

A:

Q: Express the region as a union of Type I or Type II regions and evaluate the integral ffy dx dy. YA 1…

A:

Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

A:

Q: 9tind the voleime of the s0lid generated by revolving the region bounded by the given lines and…

A:

Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curvex² = 4y %3D OA 3 О В.…

A: The shaded region shown in the figure is the area of integration

Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

A:

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: Consider the region enclosed by the curves y = a2 +1 and y = 2r + 1:

A:

Q: Let F = (-z2, 2zx, 4y - x2}, and let C be a simple closed curve in the plane x + y + z = 4 that…

A: Given F={-z2,2zx,4y-x2}. Curve in the plane (s) = x+y+z=4. Area enclosed is 16.

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: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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: Compute where Cis the counter clockwise oriented boundary of upper-half unit disc D. 0.66666666667…

A: We need to find ,  ∮ y2dx + 3xydy , over  C ,  where C is the counter clockwise oriented boundary of…

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: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

A:

Q: Find the areas of the regions 1. Bounded by the spiral r = 0 for 0 < 0 < T r = 0 2'2 х (п, т)

A:

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: 1) Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X…

A:

Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.

A:

Q: Prove that: 1- Cos (2) dxdy (¹) where R the region bounded by x+y=1,x=0.y=0

A: Given integral I=∫∫Rcosx-yx+ydxdy Where R is bounded by x+y=1x=0y=0

Q: Sketch the regions enclosed by the given curves. y = 4 cos(7x), y = 4 sin(14x), x = 0, x = T/14 y y…

A:

Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.

A:

Q: Sketch the region enclosed by the given curves. y = 3D 4 cos(5x), у %3D4 —4 cos(5х), 0 < x < T/5

A:

Q: While evaluating the area of the region bounded by two curves Vy = z and y- 11z + 24 = 0, the values…

A: Given curves are: y=x   ............................(1)&amp; y-11x+24=0  ..............(2)

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

A: Use greens theorem

Q: The area bounded by the curve y = In(z) and the lines z = 1 and =2 above the z -azis is %3D square…

A:

Q: Sketch the region enclosed by the given curves. y = 5 cos(3x), y = 5 sin(6x), х%3D 0, x = T/6 y y 5t…

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: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

Q: Let D be the region bounded by the parabola y = x2 and the curve y = sin x, and let P represent a…

A: If the input of the function is more than one, such functions are called multivariable functions.…

Q: 3. Let D be the region bounded by the parabola y= -3 and the line y=1.F

A: The region is bounded by the curves given by: y=x2-3      and      y=1

Q: 8. Find the area of the surface of the region generated by rotating the curve y = x³ from x=0 to x=1…

A:

Q: E is the region behind the surface y = 4 – x² that is in front of the region in the xy-plane bounded…

A: Given integral: ∫∬E18x dV Given that E is the region behind the surface y=4-x2 that is in front of…

Q: Verify that [y- 2x )dx +(2xy +x²)dy = dA where C is the boundary of a region %3D R R defined by y=0,…

A:

Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…

A:

Q: Q1 Verify that [(v ²– 2x )dx +(2xy +x³\dy = | dA where C is the boundary of a region %3D дх ду R…

A: By  apply green theorem

Q: O R is the region bounded by x² + y – 4 = 0 and x – y +2 = 0 an is revolved about y = 0.

A: We use washers method to find the integral of that evaluate the volume of the solid of revolution.

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

A:

Q: Evaluate the integral ₁²+ y (x+y)e³-²dA, where R is the region bounded by the lines z+y = 1 and 2 +…

A:

Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

A: