1. Find the area common to both r=2 and r=4 cos 30 11A 6. Зх 101

Q: Find the area in the first quadrant that is inside the circle r = 4 sin 0 and outside the lemniscate…

A: We need to find area.   NOTE - As per our guidelines we can solve one question so please upload…

Q: Graph the limaçon. Oval limaçons r = 2 + cos u

A: Given- r=2+cosθ To sketch- The graph of the above limaçon.

Q: r2m 1 de 1 + 0.5 sin 0 2.

A: We have to find the value of definite integral.

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 do. 1+8 cos? 0

A: Note:-  cosθ=eiθ-e-iθ2 Residue Theorem:- ∫Dfz dz =2πi ∑k Res fzk=2πi×sum of residues   Given that…

Q: Find the area Inside the lemniscate r = 6 cos 20 and outside the circle r = 3.

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Calculate the length of the side XY given the following data for 29°: Sin 29° = 0.485 Cos 29° =…

A: Solve for xy

Q: Find the area of the region outside r = 9 + 9 sin 0 , but inside r = 27 sin 0. 24T

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

Q: 4.3 Use the calculus of residues to evaluate the following integral r27 1 1+8 cos? 0

A: We find the given integral by using calculus of residues.

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

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Q: QUESTION 4 dy Find if da 1- cosh a 1+ cosh a

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Q: Find the areas of the regions . 1. Inside the oval limaçon r = 4 + 2 cos u 2. Inside the cardioid r…

A: Replace the variable u with θ The area inside the oval limaçon is given as, Where, a=0 and b=2π…

Q: 4. Find the area of the region that is in the interior of the two cardioids, 'i =1+sin(0) and r,…

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Q: 4. Find the area common to the circler=3 cos 0 and the cardiod r=1+ cos0.

A: Find points of intersection and solve the given problem. A detailed solution is given below.

Q: S= The integral dx can be transformed to which of the following when trigonometric substitution is…

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Q: Find the area of the region outside r = 7+ 7 sin 0 , but inside r = 21 sin 0. Preview

A: Given Data The outside function is r=7+7 sin θ. The inside function is r=21 sin θ.   Equate the…

Q: Evaluate the integral. 1/2 | [6 cos ti-3 sin tj+ sin 3t k] dt 1/2 | (6 cos ti- 3 sin tj+ sin? 3t k]…

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Q: Find the area of the region outside r = 6+ 6 sin 0 , but inside r = 18 sin 0.

A: The given curves are,r=6+6sinθ=r1(let)and r=18sinθ=r2(let) We need to find the area of the sketched…

Q: 5. Find the total area between r = 4 sin(0) andr = 7 sin(40). %3D %3D

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Q: Find the area lying outside r = 4 cos 0 and inside r = 2+2 cos 0.

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Q: 4.) Find the area inside the circle r=v2sin (0) and the lemniscate r2 = cos(20)

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Q: Which of the following is equivalent to / Isin(Inx?)]²dx , sin(Inx 14) dx A sin2(Inx 14) dx O (sin…

A: Given that, The given integration is following, I=∫[sin(lnx7)]2dxx We have to find the equivalent of…

Q: b) Find the common area between r= 4 cos (0) and %3D r=2 sin (0).

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Q: The area between the two loops of the limacon r = 1 + 2 sin 0.

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Q: Which of the following areas are equal? Why?

A: 1.

Q: Determine the area enclosed by the following r = 2 + cos 0 97/2 r = 4 + 3 sin 0 7/12 + V3/16

A: The formula for finding the area bounded by a polar curve isA=∫02π∫r dr dθ, where…

Q: 4. Given AB is tangent to OP, AB = 12 and CB = 8. %3D a) Find the area of APAB. b) Find mLAPB (round…

A:

Q: T/2 COS z xp V4 - sin? a

A: givenI=∫0π2cosx4-sin2xdxsubstitute  sinx=t therefore limits will change t=sinπ2=1  to t=sin0=0after…

Q: 6. S cos³ y cot y dy

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y<0 and we need to prove that | eiz | >1 For b part, we need…

Q: 2. Find the area enclosed by T = @ cos 30-

A: We need to find area.

Q: Find the area inside r = 2(cos 20- sin 2 0) and outside r 1 %3D

A: The area inside r2=2(cos2θ-sin2θ) and outside r=1 is:

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 1+8 cos? 0

A: We have to solve the integral by residue formula

Q: The integral of the right hand member of the first order LDE A B C с D -2sin³0 3 COS 2 2sin³0 3 sin…

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Q: Evaluate the iterated integral. (T/3 cos(0) 3r? sin(0) dr d0 Jo

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Q: Evaluate cos dV, where E is the region enclosed by the E sphere p = cos(4).

A:

Q: Evaluate the triple integral: 元 SS1² S² π/2 O 0 12p sin p cos 0 dp do do

A: The answer is given below:

Q: 7. Find the area of the region that lies inside both of the circles; [Ans: }( – 1)] r = 2 sin 0, r =…

A:

Q: that inside (i = 3Sing) 1- Find the area of the region that inside (ri= 35im end also Inside (rz =…

A: Find the area

Q: 2 To evaluate the integral (384 + 576 sin(t) + 216 sin (t)) dt, we recall the trigonometric…

A: Here we have to integrate the given Integral.

Q: Find the area of the region outside r = 9 + 9 sin 0 , but inside r = 27 sin 0.

A:

Q: What is the area inside the cardioid r= 2(1+ cos(4)), outside the circle r = cos(4)? 23л 11T 217 a)…

A: According to the given information, it is required to find the area inside the cardioid.

Q: Suppose that the volume, V, and radius, r, of a sphere are changing with respect to time and satisfy…

A:

Q: 4.3 Use the calculus of residues to evaluate the following integral 2m 1 de. 1+8 cos? 0

A: We find the given integral by using calculus of residue.

Q: Evaluate the following integral: ∫(cos⁡?)^5 dx    Pie/2 uppper  0 lower Where: sin(pie/2)=cos(0)=1,…

A:

Q: Find the area inside the larger loop and outside the smaller loop of the limicon ? = 1 + 2 cos ?.

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Q: (1) Find the area of the hypocycloid F (t) = (cos³ (t), sin® (t)), te [0, 27].

A: Given The given hypocycloid is r¯=cos3t,sin3t, t∈0,2π. Apply formula A=∫D∫dA=∫Cx dy+0 dx=∫Cx dy

Q: 4.3 Use the calculus of residues to evaluate the following integral 2 1 1+8 cos? 0

A:

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: 5. Find the total area betweenr = 4 sin(0) andr = 7 sin(40). %3D %3D

A: