Show that in the following problems, the line integrals are independent of path of integration and uate the integrals. (1- sinxsiny)dx + (1+ cosxcosy)dy, A(n/4,n/4), B(t/2,0). (3x2 + 2xyz)dx + (1 + x²z)dy + x²ydz, A(1,1,1) to Bf-2,-3.-4),

Q: Verify Green's Theorem by evaluating both integrals Lv² dx + x² dy dA ax ay for the given path. C:…

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Q: S, (3x² – 3yz + 2xz)dx + (3y² – 3xz + z²)dy + (3z² – 3xy + x² + 2yz)dz Calculate the curvilinear…

A: Let's find.

Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: Show that the following line integral is path independent and evaluate its value. Show the details…

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Q: Write down the new limits of integration for the integral -1 -1-y IIL" S(7,4, 2) dz dy dæ if the…

A: As per given tripple integral  0  ≤  z  ≤  (1 - y)  x2  ≤  y  ≤  1  -1  ≤  x  ≤  1   Thus, curves…

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) a…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y - x) dx +…

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Q: Evaluate the line integral (-3x+y)dx + (x + 3y)dy, where C lies along the x-axis from x = 0 to x = 6

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Q: Show that (2x In yz-5ye") dx-(5e* -x²y)dy +(x²z- +2=) dz, where C runs from (2,1,1) to (3,1,e), is…

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Q: Q.4 Show that in the following problems, the line integrals are independent of path of integration…

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

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Q: Calculate $o (3x + 5y - cos(y)) dx + x sin(y) dy if C encloses a region of area 4.

A: To evaluate the given integral.

Q: Verify Green's Theorem by evaluating both integrals aN dA |v² dx + - x² dy ax ду for the given path.…

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Q: What should be i for the path independent of (24) ´ry + A 21y – 1 dy (12) over evaluate the integral…

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Q: What should be A for the path independent of (2,4) 2Ay – x dy. y? XY + A (1,2) over evaluate the…

A: Consider the provide integral,

Q: @ Evaluate the integrals Jsx+y+2, dz dy dx-

A: Note:-   as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Evaulate the line integral of c (x^2+y^2) where c is the line segment from (-1,-1) to (2,2)

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: Sketch. the.region.cf.integratizin.and.evaluabe. thaw .. fallowing. integrals a ..... in2 Ins 2X-년…

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Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

Q: 3) Show that the line integral is independent of path and then evaluate the inte S, sin y dx + (x…

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Q: Find the complete integral of 1 az z dx, 1 dz z dxz 1 dz =x1 x2 X3. z dxz

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Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

Q: Compute the line integral of f(x)=2x over the curve y=x^2 from (0,0) to (1,1)

A: Given query is to find the the line integral for the y = 2x over y = x2.

Q: Find the value of the line integral 6xy dx + (3x² + 4y2)dy, where C is an ellipse 16 + = 1 from (4,…

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √((x-x) (y -…

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Q: Find the complete integral of 1 dz 1 dz 1 dz z dxz Ixe z z dx2 = x1 X2 X3.

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

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Q: Set up an iterated triple integral equal to √3-x² | = • S√³/3 SO √√3 x² + y² 3 2-₁/4-x²-y² 2y dz dy…

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Q: Which of the following is NOT an improper integral? 0 2x of ₁7² +²22-3²² dx + 2x - 3 2x x2 2 - 3x e…

A: which of the following is not an improper integral??

Q: Verify Green's Theorem by evaluating both integrals dA [_v² dx + x² dy = [ ] (ON-OM) DA ду for the…

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Q: Evaluate the line integralſ (x + 2y) dx + x² dy, where C consists of line segments from (0,0) to (2,…

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Q: Show that the line integral is independent of path and evaluate the integral. integral C…

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Q: Verify Green's Theorem by evaluating both integrals ON √ y² dx + x² ov - [/(2x - 2M) da dA R ax ду…

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Q: Evaluate the triple integralE 7xdV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the plane…

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Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

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Q: Set up an integral for the length of the curve. x = y2 + 6y, 0 s ys 6 OS Vay2. 37 dy OS Vay2+ 12y +…

A: We have to find out length

Q: Find the partial integral. Y dy

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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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: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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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 path C given by x = 2t, y = 4t, where 0 <ts 1. Lv - x) dx +…

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Q: Evaluate the triple integral,   4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and…

A: To calculate the value of the triple integral under the given terms

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: Given the line integral,  I=∫0,03,2coshx23+y248xdx+6ydyI=∫0,03,28xcoshx23+y24dx+6ycoshx23+y24dy We…