(2 dr z²–10z+15) Integrate:

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

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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: Q0 Integrate 2 from x? o to L x²_2 trapezaidal rule with four

A: SolutionIntegrate x2-2 from 0 to 4using the trapezoidal rule with 4 bandsFormula of trapezoidal…

Q: Calculate the double integral. 4x dA, R = [0, 4] × [0, 1] 1 + xy

A: The given integral is ∬R 4x1+xy dA  where R=0,4×0,1. Evaluate as follows.

Q: Evaluate the double integral. // (2x + y) da, D = {(x, y) | 1 s y s 4, y – 3 sxs 3}

A: Evaluate the integral

Q: V24z – 2z3 dz dy dæ, by changing the order of integration to dæ dy dz.

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Q: Find the solution in the form of Fourier integrals: U4-3uzz = 0, |u(x, t) bounded as x → ±0, sin r…

A: We are given the following second order partial differential equation : ut - 3uxx = 0  ;  -∞ < x…

Q: Choose the correct answer by changing the order of integration of the following iterated integral…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let…

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Q: Calculate the double integral. 2x dA, R = [0, 2] x [0, 1] R 1 + xy

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Q: Calculate the double integral. 3xy? dA, R = -{(x, m10 sx 5 3,-25 ys 2} -2 s ys2} .2 + 1

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Q: 2z+1 37 Prove the equation through integral calculatipns. dz < 5+z? 2

A: We will do the proof step by step.

Q: In the integration of (csc 3t)(cot 3t) dt, what is t O cot 3t none of the above O csc 3t O (csc…

A: See the details solution in below

Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 < y< 2, y – 1 < x < 1}

A: Double integration

Q: Evaluate fz² In z dz using integration by parts 2 Onz-+ +c Oz-+ Onz-+c Oz² Inz - 2 + c

A: ∫z2lnzdz=∫(lnz)z2dz=(lnz)z33-∫1zz33dz+c=(lnz)z33-∫z23dz+c=(lnz)z33-13z33+c=(lnz)z33-z39+c=z33(lnz)-z…

Q: Consider the following integral 3dx V(16 + 4.x2 )5

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Given DE is 2x2xdx+ydy=8xdy-ydx..........(1) We have following formulae, dyx=xdy-ydxx2 and…

Q: Calculate the double integral. 3xy2 dA, R = {(x, y) | 0 s x< 1, -2 s y s 2} x2 + 1

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Q: 16. Let D-((, y, z):05zs2, 0≤ y ≤1, 05:5z+y). Find the triple integral: 72xy³ dv.

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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: Evaluate the integral: ∫ t2 sec2(9t3 + 1) dt

A: The given integral is, ∫t2 sec29t3+1 dt. Apply the u-substitution by taking u=t3. Then dudt=3t2.…

Q: Integrates PDE SE ニー Zく Z8 te

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

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Q: dx 6. J Vx2-4x+13

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Q: 1. Evaluate the integrals (a) fxsin 2xdx, (b) f(3x - 1) eª dx, Hint: Use the Integration by Parts. 3…

A: SOLUTION-

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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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: What is the integrating factor of 2 (y- 4x) da + rdy + xdy = 0? O 2x

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: compute J secx dr. I n trying to integrate

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Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

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Q: And And where What is the produc A C sdR = dxi + dyj + dzk 3 Ã = zi – xj – yk Cya S. Ā.dR of…

A: Ans = 11/2  For detail go through the solution

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: Calculate the double integral. 8x dA, R = [0, 8] × [0, 1] 1 + xy

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Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: Calculate the double integral. SSR 6x / 1+xy dA, R = [0, 6] × [0, 1]

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Q: Calculate the double integral. 16 9(1+x²) 1+ y² dA, R = {(x, y) | 0 ≤ x ≤ 5,0 ≤ y ≤ 1}

A: Please see the below picture for detailed solution.

Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: Calculate the integral of 2 dt

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Use by exact form

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: Evaluate the integral: [(4 t³ - 9)i+sec² t (t³+4)3 k]dt +

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Q: Evaluate the iterated double integral. I 3 3y be dady A

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Q: Find the partial integral. (3х + 5y) dx

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Q: Use the substitution formula to evaluate the integral. 2/5 dt v/252 -1 -2/5

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Q: Calculate the double integral. 3ху2 11 3xV²_ DA, R = {(x, y) 10 ≤ x ≤ 3, -2 ≤ y ≤ 2} d R + 1

A: We have to calculate the double integral∬R3xy2x2+1dA R={(x,y)∣0≤x≤3,-2≤y≤2} In order to find the…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

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Q: (х3 + 2у — z + 3) dxdydz 0, 1 2

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: