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

Q: Calculate the integral of the line K = (3z + z – 2)dz Where C It's the curve y = x? from x = 0 to x…

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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: Q4 a) Verify Green's Theorem in the plane for f (xy+y²)dx + x²dy, where 'C' is the closed curve of…

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Q: aluate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Solve integral by changing in terms of t

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

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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: Evaluate the integral (+ 2) dz where C is the line segment from the origin to the point 1+ 2i.

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Q: Evaluate the integral ∫Cydx−xdy over the curve C parameterized by r(t)= (cost,sint), 0≤t≤π2.

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Q: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: Evaluate the line integral, where C is the given curve. | 22 dx + x2 dy + y² dz, C is the line…

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Q: The region D is bounded by the curves y = 5, and y = 5x². Which of the following can be used to…

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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…

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Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

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Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: Evaluate the line integral, where C is the given curve, (x + 9y) dx + x2 dy,  C consists of line…

A: Consider the line integral,

Q: *0 = x = 0, y = 1, x = y about the line y = 1 can be computed using the method of disks or washers…

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Q: Find the path y = y(x) for which the integral 1. r2 VaVi+y(xdx is stationary.

A: The path y = y(x) for which the integral is stationary satisfies Euler’s equation given by,

Q: Evaluate the line integral along the curve C. [(x+3y)dx + (x-y)dy, C: x= 2cost, y = 4sint, 0≤ts-…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1. + 3у?) dy

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Q: Evaluate the triple integral. 10x dV, where E is bounded by the paraboloid x = 5y? + 5z2 and the…

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Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curve y² = 4y %3D OA3 O B.…

A: To find: The value of ∫xydxdy over the region bounded by x- axis, ordinate x=2 and the curve x2=4y.…

Q: Evaluate the line integral along the curve C. (y + z)ds, C is the straight-line segment x= 0, y =…

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Q: 1+y dy

A: We can solve the given integral as follows:

Q: Calculate the integral of C being the curve given below. y= 3+x y= 3-x 6x dS C

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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 R whose area is given by the double integral. 9. 3 6. dy dx

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Q: Let S be the surface area generated by revolving the curve y = Vx, 2 < x < 12 about the x- axis.…

A: This formula is used

Q: Calculate the line integral ∫Cyxdx+dy over the curve y=lnx in the interval 1≤x≤e (Figure 4).

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Q: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

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Q: Evaluate the line integral, where C is the given curve. |(2y3 - Vx)dy, c is the arc of the curve y =…

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Q: Evaluate the integral a sin y ds where C is the line segment from (0, 3) to (4,6),

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Q: The area of the surface generated by rotating the curve y = 2 + e*, where 1 < x < 2, about the…

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Q: Evaluate the line integral (y + z) ds along the curve C defined by the straight-line segment æ = 0,…

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Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

Q: find the line integral for f = 2x + 2z along the curve x = t2 . y = 3t .z = 2t? where 0<t<1.

A: The objective is to find the line integral for f=2x+2z along the curve x=t2, y=3t, z=2t2 where 0≤t≤1…

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: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: Find the area of the surface generated by revolving the curve x = 4 1 from 8y 3 < y< 5 about the…

A: When a function is of the form x=g(y) and you are revolving around the x-axis, the interval is c≤y≤d…

Q: Find the value of integral F dr,where C is the semicircle parameterized by F(t) - (cost, sin…

A: We calculate the given integral.

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the…

A: here, E is bounded by the paraboloid  x=7y2+7z2  and the plane x=7.    so , at    x=7 ,     y2+ z2…

Q: 4. Evaluate the double integral D where D is enclosed by the curves y = a², y = 3x.

A: First we will draw the graph for given curves from that we will find the limits of x,y as shown…

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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Q: Evaluate the line integral along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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Q: Jy Find the area of the inner loop of the curve r = 9 cos 0 - 4 by using double integral.

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Q: Find the area bounded by the line y=4 and the curve described parametrically by: x(t) =…

A: Given: y=4x(t)=t-1t,    y(t)=3t+1tSince y=4,  y(t)=3t+1t ⇒ 3t+1t=4⇒3t2-4t+1=0⇒3t2-3t-t+1=0…

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

A: Greens theorem