Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x – y) dy for the given path. C:…
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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…
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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…
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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…
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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,
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Q: Use Green’s Theorem to evaluate ∫ sin 5y dx + 5x dy around the boundary curve C of the region R,…
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Q: Express the region as a union of Type I or Type II regions and evaluate the integral ffy dx dy. YA 1…
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Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…
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Q: 9tind the voleime of the s0lid generated by revolving the region bounded by the given lines and…
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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…
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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:
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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 +…
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Q: 1. Evaluate , 3y e ²x dA where D is the region bounded by x = ₁x = 1, y = 1 and y = 2. 2
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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…
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Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…
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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)
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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…
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Q: The solid bounded by y = 4, z = x², z = 2y, and z = 4.
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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…
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Q: Compute 6xy da dy, where D is bounded by the curves y = 4 – x2 and y = 2x + 4.
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Q: Sketch the region enclosed by the given curves. y = 3D 4 cos(5x), у %3D4 —4 cos(5х), 0 < x < T/5
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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)& 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…
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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…
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Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.
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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…
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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,…
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Q: 2. Evaluate , dV, where o= 45 x²y and V is the closed region bounded by the planes 4x + 2y +:=8, x=…
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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+
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Q: Evaluate the integral ₁²+ y (x+y)e³-²dA, where R is the region bounded by the lines z+y = 1 and 2 +…
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Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…
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- Sketch the region enclosed by the given curves. y = 2 cos(6x), y = 2 − 2 cos(6x), 0 ≤ x ≤ π/6What is the amount of the rotating body formed by rotating the region bounded by the y = cos x function, the line y = 3, the line x = pi / 2 and the oy-axis around the ox-axis?Calculate SC F · dr, where F(x, y) = <x3 + y, 9x − y3>and C is the positively oriented boundary curve of a region D that has area 8.
- Consider the region in the xy plane bounded above by the parabola y=25-x2 and below by the line y=x+5Compute the integral ∮C [(cos x − 3y) dx + (2x − sin y) dy],where C is the closed curve that travels on the line segments from(0, 0) to (4, 0), from (4, 0) to (2, 1), and from (2, 1) to (0, 0).The shaded area shown in (Figure 1) is bounded by yy axis and the curve y2=(1.44−x)m2y2=(1.44−x)m2 , where xx is in mm. Suppose that aaa = 1.44 mm and hhh = 1.2 mm
- Use Green’s Theorem to evaluate ∫ sin 5y dx + 5x dy around the boundary curve C of the region R, where R is the triangle formed by the point (0, 0), (1, 1) and (1, 3).Let D be the region bounded by the parabola y = x2 and the curvey = sin x, and let P represent a path going around D counterclockwise.Compute ∫P F ·dr where F(x,y) = ∇f and f(x,y) = x2ye4x−y^2.Compute the line integral∫C [2x3y2 dx + x4y dy]where C is the path that travels first from (1, 0) to (0, 1) along the partof the circle x2 + y2 = 1 that lies in the first quadrant and then from(0, 1) to (−1, 0) along the line segment that connects the two points.
- What is the absolute extrema of Q(y,z) = y2z2 on a region with vertices at the points (0,0), (0,4) and (4,0)?8.2) 7) The given curve is rotated about the yaxis. Set up, but do not evaluate, an integral for the area of the resulting surface by inte grating (a) with respect to x and (b) with respect to y.