Q.1) Evaluate the following integral 2dx J r (3(In r)2 + 12 In r- 15) |

Q: a) Solve the following iterated integrals holding Fubini's Theorem. 1. 1 '(x+y)dydx

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Q: 2. Evaluate each of the following line integrals in two ways∗ . (a) Z C1 F~ 1 · d~r, where F~ 1(x,…

A: Given vector field is F→(x,y)=(2x-cosy)i^+(xsiny)j^F→.dr→=(2x-cosy)dx+(xsiny)dy C1 is the…

Q: Example: Evaluate the following Integral CO -x=V2 ry=2 x³ev° dydx Jy=x²

A: Here we use change of order to solve this

Q: 2 2et 5 Let 7(t) 5, Evaluate the definite integral. %3D 13 | F(t)dt = ( 6.

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Q: 3 Evaluate the integral de using the two-point Gaussian quadrature rule O -|4 1035 N/N N/W 끔

A: We have to evaluate the integral ∫−3311+x4dx by using two-point Gaussian quadrature rule. Here,…

Q: If g(1) = -1, g(5) = 2, and | g(x) dx = -9, evaluate the integral %3D æg'(x) dx.

A: Given: g1=-1  and g(5)=2∫15g(x)=-9

Q: 22. Evaluate the iterated integral. (b) f. [, 2x + »)'dy (a) x+y+ xy dydx

A: Now we will solve the given double integral  We know integration of Xn dx = X(n+1) / (n+1) + C ,…

Q: Evaluate the integral 5a2 - x+27 da. (x2 +9) 5x3 x2 + 27z) · In|r(x² + 9)|+ C 2 3 In |피 + 2z In |2…

A: Topic - indefinite integration  Note- as per our guideline if more than one question uploaded only…

Q: 9) -423 dA 5.evaluate the Following double integrals. 1. where R-

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 1 6. Evaluate the given integral using suitable substituion COs(V도+ 3) dr

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Q: Consider the improper integral and the propositions dx J = = 6of foo x² + 3 1- The integral J…

A: Find out the correct statement.

Q: Evaluate the integral.

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Q: J Express the interval in (a-R, atR)d 1 x_- alcR and

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Q: 2x Evaluate the improper integral J dx, if it exists. (12 + 81)2 -00

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Q: 4 – dt 2 cos 4t 1.

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Q: 8. Evaluate the integral S xydx from x=3 to x=6 when x = 6cos0 and y = 2cose A. 9/7 B. 9/3 C. 5/3 D.…

A: Topic:- integration by substituting

Q: (C) The evaluation of the integral S. de is 0 cos3e (i) 글+in 3 3. 4 (ii) +=In 3 4 3 (iii) None of…

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Q: 19. fy/6 + 4y – 4y² dy

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Q: 6. Let r>0. Evaluate the following improper integral:

A: the given integral is ∫-∞∞rr2+x2dx First solve the integral ∫rr2+x2dx r∫1r2+x2dx substitute x = ru…

Q: 1- Find the integral of: 2 cot - de T/2 A- B- / dr Vr

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Q: Evaluate the integral. et i + 3t2 j + In(5t) k) dt + C

A: We have to evaluate the given integrate…

Q: 1. Evaluate the iterated integral. .Só Sa(x² + y) dyd.x b. S So sin(x²) dydx 2y -1 x+1 dydx с.

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Q: 2.3 Use the Cauchy integral formulae to evaluate 22 -1 J (9 – 2ª)(2 + 2i))* where C is a circle |2 +…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: 19.23. Evaluate the integral , dz/(z – 1 – i) where y is: (a) the line joining 3; and (b) the path…

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Q: +0o 34 Evaluate the imporper integral f10 , dæ divergent 17 In 9

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Q: Consider the following propositions associated with the study of the +∞ dx J - 1.1² √6 +1 improper…

A: Given : ∫1+∞dxx  in which 1x6+1≥1x

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: Evaluate the integral. 3t-2 clt to t +1

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Q: 2. Evaluate these indefinite integrals: dt (d) S; dt 2t2+5t+3

A: Given that a integration  and we solve it by using general property of integration. Here i attached…

Q: Evaluate the indefinite integral (7t)cos(10t) dt %3D + C

A: 2 cos(A)sin(B) = sin(A+B) - sin(A-B)

Q: Q.1) Evaluate the following integral 2dr (3(In r) + 12 ln z -15)

A: Given:∫2x3ln2(x)+12ln(x)-15dx=23∫1xln2(x)+4ln(x)-5dxNow solving∫1xln2(x)+4ln(x)-5dxsubstitute…

Q: Evaluate the integrals of five only of the following: 1) I = St2 e" dt 2) I = Se-2x sin 2x dx 3) I =…

A: Please refer the attached image for complete solution.

Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 a. dz S dz b. So 22(2-1)" z(z-2)4…

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Q: Evaluate the integral. 2 2 t+ dt 15 OA. 29 О В. 6

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Q: 2_ Calculate the generalized integral. x In r dx J. (1+12)3

A: The given integral: Calculate the above integral:

Q: For n EN,n> 1, making a suitable variable change in the integral sen"r cos³ xdx, ,it is obtained…

A: Explanation of the answer is as follows

Q: 2 2. Evaluate the iterated integral 6x'y dady

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Q: 3. Evaluate the integral o f(z) dz, where C is the unit circle enclosing the ori- gin, and f(z) = 1+…

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Q: Evaluate the integral: -2e 2е π/3 ₁² /³ tlnu tans ds du dt 0

A: In this triple integral we first integrate with respect to 's' then with respect to 'u' and in last…

Q: Evaluate the integral. 1 8 dt V15-21-? - 1 OA. 6 В. O C. 4 D. 3" O D. co fm

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Q: Evaluate the integral. 2 [ 11t sec-'t dt 2/√√3 2 S 11t sect dt = [ 2/√√3 (Type an exact answer,…

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Q: 7. Evaluate the following integrals : (») f (- 4 - z) dz, (a) z – 1 |z|=3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2 Evaluate the definite integral Зх + 4 dx 11 5 17 17 2 ךי" יזנ 3.

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Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

Q: _4. Evaluate the following integrals. 1 31 1 2-x 2-x-y a) //: b)// y(x + z)dzdydx dzdydx -1 2 0

A: Evaluate the following integrals a)∫-11∫23∫01yx+zdz dy dxb)∫01∫02-x∫02-x-ydz dy dx

Q: 37. Evaluate the integral fи 4x³y dx + x* dy for any closed path C.

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Q: Use residues to evaluate the integral 2T 1 de. %3D 5+3 cos 0

A: To evaluate : ∫02π15+3 cos θdθConsider unit circle |z|=1i.e. z=eiθ⇒dθ=dzizAlso, we use cos θ=z2+12z,…