Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass through the origin

Q: Evaluate the integral: (t i-tj+3t k) dt

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Q: Q2. Evalnate the double integral SS хе ク over the finite regieon 2 R={(x)): x2, y54ーx3

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Q: Evaluate the integral. 1 dt t3 V2 -4

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Q: Use the specified substitution to find or evaluate the integral.

A: We need to use the specified substitution to find or evaluate the integral.

Q: Then the integrand decomposes into the form d + x + 2 c ax + b+ 2 where a = b = C = d = Integrating…

A: Partial fraction and indefinite Integration

Q: Find the partial integral. + 3y?) dy t.

A: Given that a  integration and we solve this integration by using general formulas of integration. We…

Q: 1 Show J xd|x| = 1, by definition of RS-integral. %3D -1

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Q: If fx is the integral t^2 dt from (x,x^2) then: f'x =  f'(-2) =

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Q: Compute for the nonhomogeneous linear DE. d²s ds + dt2 s = 0, dt ds = 0, t = 0 a. 4t + 2cost %3D dt…

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Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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Q: Evaluate the integral ∮C 4x3y dx + x4 dy for any closed path C.

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Q: (a) Compute the multiple integrals of (i) V4-z2 1 xy dxdydz (11) SS, (8 – x² – y²)dA, where R = {(x,…

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Q: Evaluate the integral (6x-y)dx + (x+6y)dy along the path C, defined as y = 16-x² from (0, 4) (4, 0).…

A: Answer: The solution is given below:

Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: Evaluate the integral. dt V 4 + t2

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Q: Evaluate the integral | t(sec t2)4 dt

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

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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: Evaluate the integral. integral t e -3t dt

A: Let given integral be - y = ∫t e-3tdtUsing by parts to integrate the above integral - ∫uv dx = u∫v…

Q: Find the product of the integral 1- S x²cos(xy)dxdy

A: We have to change order of integration first.

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

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Q: ¡(z+1)dz 3 where C is z+2|= |z+2\=% z'-4z

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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: Find the line integral of F =9xy*ï +(x² + 3),yj over the path L.

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Q: Calculate the iterated integral. 2/s+t ds dt

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Q: Evaluate the integrals in Exercises 9 and 10. 9. 8x sin y de – 8y cos x dy C is the square cut from…

A: Explanation bye green's theoram in plane, we have  ∫∫R(∂N∂X-∂M∂Y)dxdy = ∮Mdx +Ndy compare the…

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

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Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: Let H(x) integral ,for -2 ≤ x ≤2.Evaluate H(0).

A: Consider the given integral, Hx=∫0x4-t2dt use the substitution method to solve the above integral as…

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

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Q: 15. Evaluate the line integral J.(3xy* - 6xy ]dx + (4x°y³ - 3x?) dy, where C is any path from (1,2)…

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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: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 7y2 + 7z² and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: is Theorem 1.6. The line integrals of f in D are independent of path if and only if f has an…

A: Given: The line integrals of f in D are independent of the path if and only if f has an…

Q: 5, find the line integrals along the given path C. In 13. | (x – y) dx, where C: x = 1, y = 21 + 1,…

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Q: Verify Green's Theorem by evaluating both integrals ам √₁ y ² dx + x² dy = √₂√ √ (³x - dA ax ду for…

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

A: This question is related to vector calculus solved in step 2.

Q: Expand, that is, perform the indicated operations on the differential operator D. 1. xD(R+ x)

A: Given that         xD(D+x)  Here we have to expand this and perform the indicated operations on the…

Q: Evaluate the line integral along the given path. (4x-7y)ds C:r = 7ti+6tj, 0 ≤ y ≤8 O-454/85 O-444√85…

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Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

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

A: We have  I=∫(0,0)(3,5) cosh(x23+y25)(10xdx+6ydy)apply Green's…

Q: Let f(x, y,z) = x? sin y+y e, where x = t+3,y = net-1 and z = In 2t. %3D at t = 1 is: df dt О 12п O…

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

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Q: Compute the following Cauchy principal value integral: dx р.v. x4 – 1 п/2 -T/2 Зп /2 -27

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Q: Suppose that f(c, y): at which {(x, y) | 0 s< 1, - a <yS vE}. 1+ x Then the double integral of f(x,…

A: According to question given that f(x,y)=y1+x at which {x,y) |0≤x≤1, -x≤y≤x

Q: Evaluate the integrally.dy.W 6y+ 34

A: To evaluate

Q: Evaluate the integrals in Exercises 9–12. 4 cos (x²) dx dy 2y 9. e dx dy y/2 10. 27 sin 7x² -dx dy…

A: Given: