The particular integral of y" + 5y' + 4y = 3x + 2 is (A) 3х+ 4 (В) 3х — 7 3 (C) 4 (D) 4 - 16 4.

Q: Q.3 Find the double integral for Sl. x2 dydx, where R between y = -4/x y = -x and x = -4

A: Ti evaluate the given double integral  first we draw  the region

Q: Find the integrals by the method of partial fractions. x² – 3x + 4 dx ·J (a +1)(x – 1)(r+2) 1. 5х —…

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Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² –…

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Q: (2x+5)² 19. What should be the rewrite of the integrand of S -dx so that the resulting integral is…

A: Given query is to rewrite the integrand in integrable manner.

Q: 2. Suppose | 29(r)dr = 10. Using linearity properties of integrals, calculate | (g(x) + 3)dx. 3

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Q: 1. Evalute the improper integral 3x dx. 1+ x2 -1

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Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

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Q: 1 Suppose we perform the substitution u=3+Vx in the integral dx . I (3+ Vx)4 What is the resulting…

A: we have to find the given integral

Q: 2.) Evalvate the Integral ودل أاد-ل (x² _33² dx, .3 2 by making w - x²-3 NOTE: Answer should be in…

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Q: Evaluate the integral. 9. dx J2 (x² - 1 1)3/2 Additional Materials Type here to search

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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: Evaluate the integral +2 zp; :- 2 in the two cases: 1) y = {z :|2| = 1}; 2) y = {z : |2| = 3}.

A: We will evaluate it by Cauchy Residue Theorem Let R be the residue then ∫f(z) dz = 2π i R Firstly,…

Q: 4. Show that evx dx = 2Vxevx - 2ev + C Hint: Make a substitution first before doing integration by…

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Q: x³ + 6x2 + x+2 2 Tan Ve fx-1 ax + In{(x+ 1)*(x² – x + 1)"| + The resulting integral of -X+ -1 + C,…

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Q: Compute the double integral , xy³ dA where T is the triangle (-1,0), (0, 5), (1,0).

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Q: Evaluate the integrals

A: Given: ∫-3-1y5-2yy3dy for evaluating this limit we first separate terms then integrate it

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: .2 What is the reversed order of integration of 1 dxdy? a. II Vx* +1 dydx 0, O b. x4 +1 dydx 0, .8…

A: Topic:- application of integration

Q: 2. Compute the integral dy dx by interchanging the order of integration.

A: Order of change of integrals

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: .3 Evaluate the integral LST wy+x*v+vz) dzdydx 0, 2.

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Q: Compute the integral: -3 dz (z – 2)*

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Q: (a) Evalate the integral||xydy dx. 12

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Q: ii) √²√³ xy² S¹S. -dydx -3 x² +1

A: Evaluate the iterated double integral.        ∫01∫-33xy2x2+1dydx

Q: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

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

A: SOLUTION-

Q: 10.) Find the integral of* 3 (-4y ) ( +14y-7) dy

A: We need to evaluate ∫3y6-4y-3y7+14y-2-76dy                          (1) Let y7+14y-2-7 = t On…

Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Consider the integral 2 6z² In(z) dz

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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: 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: 15. Express c9-x² f(x, y)dy dx as an iterated integral in the or- der dx dy.

A: first, we will write an equation we have  y=0,y=9-x2x=-3,x=3 changing it w.r.t x we have…

Q: Q2/Evaluated the integrals v2 1- f– (1-v2 )2

A: The integration of v2/(1-v2)5/2.

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

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Q: 1. Compute the given integral. Using Substitution Method 5x-12 dx = +C 5x2-24x-1 *

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

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Q: Find the total differential of z = In (2x – 3y).

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Q: xyz dy dz dx -8 -V 64 – x2 xyz dz dy dx 64 x2 -8 Evaluate one of the triple integrals. xyz dV =

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Q: v) ₁ √√¹-x² sin(x² + y²) dzdydx fő

A: Given is  ∫01∫01-x2∫01sinx2+y2dzdydx In order to solve this integral it is needed to first convert…

Q: Calculate the double integral. Te 1+ xy бх dA, R = [0, 6] × [0, 1] 1 + xy

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Q: d) Prove the results of the integrals 3 dx = 2+ In (2)– 4 [In (5)– In (3)]. x² +3x +2

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Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

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Q: The particular integral of y" + 5y' + 4y = 3x +2 is

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Q: 2. Integral A e3A dA

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