FIGURE 21 3. Which of the four regions in Figure 21 is the domain of integration for Lo s4,)dy dx?

Q: Question 19 Evaluate the improper integral: e-2 x dx a) 1 b) O c) d) -2 1 e)

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Q: Question 7 7 da a4 1 Calculate the integral: a) OIn|2 - 1| + C b) O미-1 + C 7 c) 0arctan(2) + In|(x -…

A: See the attachment

Q: Solve the following Bernoulli's D.E.: dy 3 „y = x*y3 1 %3D dx

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Q: QUESTION 7 In 2 Let a double integral ху dy dx be given. What will be th e equivalent expression if…

A: Given  We need to change the order of given double integral. We will draw the region of its given…

Q: Question 8 5-1 If the integral of what is M and N? te 20 dt is M(4e-1/4+N)' M= N=

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Q: Question 2 (a) Evaluate the following by first reversing the order of integration. Sketch the region…

A: 2.a. The given integral is ∫04∫x2siny3+cosy3dydx To find: the integration by changing the order of…

Q: QUESTION 9 Use the Fundamental Theorem of Line Integrals (FTLI) to evaluate ending at (1,3) O a.…

A: Line integral over the curve

Q: QUESTION 2 Integrate the following integrals. a) S(3x² – 6x +4)dx b) 2cos 2x++ Vr - |dx

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Q: QUESTION 7 Evaluate the double integral. FS= 3xy 2 RX²+1 OA. 8 3 OB. 16ln (2) OC. 8ln (2) OD. 16 3…

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Q: Question 7 4dy Evaluate the integral ; 5y +2 (A In|5y +2| +C 5 (B -2미by+ 리 + C In|5y +2| + C (D…

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Q: Find the integration to de 0. a+bcos² 0

A: Given ∫02πdθa+bcos2θ. The given integrand is even function  We need to evaluate the above integral.…

Q: The value of the double integral 7 1 4xy dy dx is 4

A: ∫46(∫274xydy)dxIntregation wrt y so x will be constant.⇒∫46[4xy22]27dx ⇒∫462x(49-4)⇒∫462x(45)dx

Q: Question#4: Evaluate the following integral using the Trapezoidal and Simpson's rules with n = 10 In…

A: We can find numerical integration by using of following two rules: Trapezoidal Rule:…

Q: the area outside r = 1 and inside r = 2 cos 0 is

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Q: QUESTION 1. EVALUATE. J 1 dx V9x2+4 In (/9z² +4+3zl) +C 3 ||

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Q: - Find the area of region A in Figure 19. r=4 cos e r= 1 -1 14 FIGURE 19

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Q: Question 1 Calculate the integral: /3x In (x°) dx a) O In(x*) + C 3 b) O* In(x*) – r + C In(x*) + *…

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Q: Question 3. Compute the following integrals. 3.1. S(4x2 – 1)'x dx - 3.2. Sx e5x dx 3.3. S x?cos xdx

A: 31) The given question is =∫(4x4-1)4xdx now first of all simplify the function. (4x4-1)4=(4x2-1)22…

Q: Question 11 A те *dz is A в D E) divergent

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Q: Question 2 Estimate the integral I sin (x) dx by the trapezoidal rule using n = 4. а) О0.7000 b) O…

A: Option C is correct.

Q: Evaluate the integral. .2 5) t + dx t 1

A: Given,   ∫12t+1t2dx

Q: 22. Compute the given integral. S sin (2x)dx

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Q: The particular integral of (D² +1)y = x is

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Q: The region inside the rose r= 2a cos 20 and outside the circle r = av2.

A: The given equation are  r= 2acos(thitha) r=a√2

Q: Question 13 Evaluate the integral: f (z² + y²) ½ dydz -1/2 O v2 + In(v2 + 1) O In(v2- 1) O v2 -…

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Q: Example 3: Solve by Laplace transform d'y +2- d´y_dy _2v= 0, y(0) = 1, y'(0) = y" (0) = 2 · %3D %3D…

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Q: QUESTION 2 Use integration by part to evaluate: In 3t dt A. t In 3t – t + C + C В. 1 + C OC. 3t С.…

A: Given: The integration ∫ln3tdt To evaluate: The given integration using integration by parts.

Q: Question 14 7 da Calculate the integral: 7a - 6) (x + 2) 8. a) ㅇ윽피-6-mlz + 21 + C 7. b) O In r…

A: Given that: ∫7(x-6)(x+2)dx

Q: O Question 17 Evaluate the integral dx (7x2 + 1) by making the appropriate substitution: dx = (7x2 +…

A: Solving

Q: In'(r) da. integration by parts (a)

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Q: Question 4 Evaluate the integral *dx, 2" -+C In2 A +C In2 B 2 -+C In2 D +C In2

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Q: Question 6 Estimate the integral 1 dx by Simpson's rule using n = 8. Vx3 + 4 a) 00.9361 b) O1.0212…

A: given integral :

Q: Question 5 5. Use the fact that +C to either evaluate the improper integral dz, or show that it…

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Q: (1+ 1)? dt =D t3

A: Given : ∫1+t2t3dt

Q: Solve the following non-homogeneous linear ODE of first order dy 2y + dx sin x

A: Given, dydx+2xy=sinxx To solve the above differential equation.

Q: dø +3ø = sin ot on (0,+∞) dt [$(0) = 1.

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Q: 1 By writing u y", and using the chain rule, show that 0") = nyn-1. dx

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Q: Question 4. Evaluate the following integral. |(r3 + 4)°3x dx

A: ∫x3+423xdx=∫x32+2x3(4)+423xdx  [expanded the square]=∫x6+8x3+163xdx=∫3x7+24x4+48xdx [distributed the…

Q: QUESTION 3 3 Given the double integral, e dxdy. 0 3y

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Q: 5. Find ffp(x + y)² dx dy, region in Fig. 17.2.12.

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Q: Question 12 Evaluate the following improper integral: 2 [ x5 A) / B) - 1/12 C) 2ln(x5) + c D) The…

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Q: Apply the techniques of Example 7.1.5 to the evaluation of the improper integral 8 dx 1 = (a) Let…

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Q: Find the integrating factor to make the following ODE exact У(2ху + е*)ӑx -е*dy %3D0.

A: Let's first check if the given differential equation is exact or not!   For the given differential…

Q: Question 1 2dy Evaluate the integral Зу — 4

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Q: Question 5. For this question consider the standard result: 1 ;du = tan¬1 u + u? (1) Only using (1)…

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Q: Question 1 For each improper integral below, show that it diverges or find its value. (a) / Valnz…

A: Solve the improper integrals, a) ∫07x lnxdxb) ∫04lnxxdx

Q: QUESTION 7 The improper integral 1 dx converges to 5 Vx-5 попе 1 O 4

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Q: Question 1 Evaluate I S Csin(0.70)dx %3D where, C = 4 x1 = 0.6 rad %3D v2 = 0 9 rad

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