5Tt/6 5 2 1 1 \ZTt/6 11T/6 4T/3 5T/3 + C 5 r =1+ cos 0 r = 1– cos 0 - find the commen area berween tham LO LO

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A: Find the area of the region inside the circle and outside the cardioid, where the equation of circle…

Q: f'uo) -22:2294 W = 0.4748 2nd Stetzation flui) = fla4748) = 31e flui)= 0.0044 f'ni)= flouT48) = -31e…

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A: We will find out the required area of the bounded region.

Q: cos (r+k) Compute de by using substitution technique where k is a cos E constant. [Hint: cos (A+ B)=…

A: Integration

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A: General equation of the cardioids is r=a(1+cosθ) and Area of the cardioids is 6πa2

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Q: 3(2 + cos t)3 +c Use the appropriate substitution to evaluate the following integrals: . sint (2+…

A: Solution is given as below:

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A: Consider the provided equation and simplify:

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Q: a) sin2021 (2mr)dr re gln z b) Ip- c) | In(csc r) cot rdr 1 d) 2r – a2 et - e- dr ez +e- e) 을 In 3…

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Q: sin³ (cos(4) dx 2 32 Ⓒcos A COS 35 32 B 35 32 Ⓒ-3 cos (4) C 32 D 3/7/7 C (4)[-5cos (4)+7] 5³ (4)…

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Q: Z1 "(cos(0, r2 Z2 02) + isin(0, – 02)](z2 # 0). 85. Let z1 = ri(cos 0, + isin 01) and z2 = r2(cos 0,…

A: Given z1=r1cosθ1+isinθ1 and z2=r2cosθ2+isinθ2.

Q: 12. Find the area of the region shared by r = 1+ cos 0 and r = 1 – cos 0.

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Q: (1+ etane) sec² e de = e TO FO 2 [0(sin(In 0) + cos(In 0))] = de csc(ln 0)

A: ∵1     ∫0π4(1+etan θ) sec2θ dθ=∫0π4(sec2θ+etan θsec2θ )dθ=∫0π4sec2θ dθ +∫0π4etan θsec2θ dθ∵∫0π4sec2θ…

Q: 67. f'(1) : s'(1) = ; – sin 1 + 2; s(1) = - + cos t+ 21 – 3 %3D

A: Given: f'(t)=12t2-sint+2; f(t)=16t3+cos(t)+2t+3

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Q: St' sin(2t*)dt (sin(2t*) - 2t*cos (2t*)) + C (sin(2t*)-2t cos (2r*)) +C 14 1 (sin(2t*)-2t cos (2t*))…

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Q: QI by the chain rule iplakdy 订 =(sin x)cox x = sin-ly+ cos(er) %3D and Find dy

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A: We have given differential equation y"+25y=0 with initial conditions y(0) =6, y'(0) =-4 We have to…

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Q: az az and as Use the chain rule to find at sin(0) Z = r = st, 0 = s6 + t6 6sºcos 6 + ,6 sin s° + t°…

A: Use partial derivative

Q: Hi, there are two questions a) and b) attached  Thanks so Much!!!!

A: (a)consider the given complex number:

Q: 5s Evaluate J|2 sin s Jdtds 0 0 I[ 2 OA. 3 (1 – sin(125)) O B. 3 (1+ sin(125)) (1+ cos(125)) 3 OC. 2…

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Q: A/6 Evaluate the integral 3cos 3t sin 3t dt. A/6 | 3cos 3t sin 3t dt = (Type an exact answer.)

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Q: The area of the region inside r = 2+ cos 0 and outside r = 4 – 3 cos 0 is given by | ((2+ cos 0)² –…

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Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

Q: dr 25. (z + 1) da 26. 1/2 V1-22 ez dz 27. In 2 1+ e2 In (cos 'z) dr (cos 1r) V1-r 28. tan z da 29.…

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Q: |(5e" + 5z* - 6 sin z)dz =- 5e" + z5 – 6 cos z+e 5e" + z5 - 6 sin z+e 5e" - z +6 cos z+e 5e* + z + 6…

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Q: Evaluate the integral. 1/2 |[cos 9t i- 3 sin tj + sin? 3t k] dt T/2 | (cos 9t i- 3 sin tj+ sin 3t k]…

A: We have function ∫0π2r(t) =∫0π2[cos9t i -3sint j + sin23t k ]dt

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Q: 3. r3D 0, 6ө > 0 34. r = 0², –2 < 0 < 2T 35. r 3 3 соs 30 36. r = -sin 50 37. r3 2 сos 40 38. r = 2…

A: The objective is to sketch the given polar equations.

Q: (§5.7, Q98) Show that the two regions in Figure 4 have the same area, i.e., show that V1 – x² dx :…

A: We have to show that  ∫011-x2 dx = ∫0π2cos2u du.

Q: 2) If z = cos 0 +isin 0 show that 1 = 2 cos 0 a) z+-D 1 b) z" + 2 cos no %3D

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Q: 1. (a) Use integration by parts to verify the reduction formula l(cos"-² x dx cos"- xsin x, n–1…

A: Solution:Verify the reduction formula∫cosnx dx=cosn-1x sin xn+n-1n∫cosn-2 x dxDerive the Wallis…

Q: I. Fill the table in. CN Z1 Z2 No. Rec Pol Exp 1. 5- j5 2. 152-34° 3. Z3 25ein 4. Z4 -13-j12 5. Zs…

A: Since you have asked multiple questions, we will solve the Q.8 and Q.9 for you. If you want any…

Q: 6. 7. 3+6s+45²-25³ s² (s² + 3) 26-5²- s(s² + 4s+13) [2+1+√√3 sin √√3t-4 cos √√3t] 2 [2-3e-2t cos 3t…

A: To find the inverse laplace of the following.6 3+6s+4s2-2s3s2s2+37 26-s2ss2+4s+13

Q: J (sin 3x)² = sin 3x xp- sin 3x CO = sin 3x xp- sin 3x On simplifying further, y2 (x) = cq sin 3x /…

A: In this question , constant is to be included in the last solution of the differential equation.…

Q: Evaluate the integral: S 13x³ cos dx CoS Choose the most appropriate answer. 78 x sin 1B³ sin - 16…

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Q: しet f(ス) be (- cos(N/2), z e[-,0) flx) = 0, (os (A/2), 2 e (0,0] [-N, w). The extan sion 4 t(a) to a…

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Q: Q1: Find the integration of : (choose 3 only ) 1. Sc (3 sin x)cos (4 sin x). cosxdx Cos

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Q: uate the erihite integrai. 1/4sin(t) dt Cos (t) COS

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Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: (a) Find all the solutions of cosh z = 4 (Hint: cosh z =

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Q: 1) LtZ be a solukion (5) of complese mumber then the sinh Z+ Coah z -e is Z=1?

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Q: g(b). Use the Substitution Formula, -g'(x) dx = f(u) du where g(x) = u, to evaluate the following…

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