What is the area inside the cardioid r= 2(1+ cos(4)), outside the circle r = cos(4)? 23л 11T 217 a) 67 b)- 4 c)- 2 d) e) 5л 4

Q: Find the area of the region Inside the cardioid r = a(1 + cos u), a > 0

A: Given  r=a1+cosu, a>0

Q: Evaluate the iterated ntegral by Lonverting to polor coordinates. 2. zy dx dy 34

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Q: Use Green's Theorem to evaluate the integral o (3x - y)dx + 4xdy where C is the circle x +y? = 1…

A: Consider the given integral. ∮C3x2-ydx+4xdy Here C is the circle x2+y2=1 The Green's theorem can be…

Q: 2Sin Cze) 4-COS S (zt)

A: The solution for the above question is as shown below.

Q: The contour of integral zdz of the cirle |z-i| =2 is

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Q: Consider the quarter-circle of radius 1 and right triangles ABE and ACD given in the accompanying…

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Q: Evaluate the integral SR 8xydA, where R is the triangle 8x + y 0, y 2 0. SR 8zy dA =

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Q: Find the area Inside the cardioid r=2 cos (6/3) and outside the circle of radius r = vZ centered at…

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Q: Calculate the area of the inner loop of r = √3 − 2 cos θ.

A: To Find: Area of the inner loop of r.

Q: Use the definition. that sinz •prove Z = UJZ %3D

A: Using definition of derivatives.

Q: | Use the Cauchy integral formulas to evaluate the eiz COS Z -dz, 2²(2z – 37)* where C is the region…

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Q: Use green's theorem to calculate the integral Fdr, F(r, y) = (e* + x²y , e³ – ry² + sen(3) + 2)…

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Q: Find the area enclosed by the loop of the strophoid r = 2 cos 0 – sec 0 -

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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: can you help me step by step please

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Q: Use Green's Theorem to evalute this integral where C is a triangle with point coordinates (0,0),…

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Q: - Find the area of the negion that inside (i=3sin@) eind also In side (rz = + sin@) ?

A: To find the area of the region inside r1=3sinθ and inside r2=1+sinθ

Q: 93. which f the follouwing repreeents ene - dimenalional heat Sqeation? 46) du c2 au %3D (d)u + azu

A: Some definitions: Wave equation: ∂2u∂t2=c2∂2u∂x2 Where c∈ℝ is called wave speed. Laplace equation:…

Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: Determine the area of the right half of the cardioid formed by r = 7+6 sin 0 14 12 10 8 6 2 -2 -4…

A: Explained below

Q: Evaluate the given contour integral, where C is unit circle z=1. 3e cosz 2z +4 -57 + 2z- 4i 3 z' +…

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Q: - Prove that the contour integral – z)dz = -12i where C is the triangle with points 0, 3i and -4…

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Q: Calculate the area of the region bounded by: r = 9 cos(0), r = 9 sin(0) and the rays 0 = 0 and 0 %3D…

A: I have provided a solution in step2

Q: (b) f(u) = tan(arccos u). FRAS SER UNIVE ERS %3D ERSI TY OF fficial que s test question question ion

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Q: Find the area of the region enclosed by the curve r = 2+ cos (20). (1.) (3,( Bu Die Aya Yard 97…

A: To find the area of the region enclosed by the curve r=2+cos2θ

Q: Show that the area of the surface of the solid generated by revolving the cardie r = a(1- cos 0)…

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Q: Consider the inetgral (11z + 2) dA where Ris the region between the circles z? + y? = 9 and z2 + y?…

A: Since R is the region between the circles x2+y2=9 and x2+y2=100. Therefore, we describes the region…

Q: Find the area of the rigion lies between the circles r=2 and r=4cos(theta) in the first octant.

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Q: Find the areas of the regions Inside the cardioid r = a(1 + cos θ), a > 0

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Q: 3. Evaluate the integral cosh ™z dz, z(z? + 1) Izl=2 where the circle |z| = 2 is described in the…

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Q: Evaluate the integral Sr 8ry dA, where Ris the triangle 8x + y 0, y > 0.

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Q: Suppose the divergence of the electric field in some spherical region is found to be V E = 5kr³.…

A: as given,   the divergence of electric field in some spherical region is ∇·E=5kr3 claim- to find the…

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dr where C is the line…

A: Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: Find the area which is outside the curve r 4 cos 20 but inside the curve %3D r = 2.(

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Q: What is the area inside r=3cos theta and outside r=1+cos theta?

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Q: Use Cauchy's Integral formula to evaluate the integral: Sa (z+1) e2z dz where C is a circle |z| = 3.…

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Q: find the area of the surface formed by revolving the cardioid r= a(1+cosθ) about the x-axis

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Q: Compute the integral using contour integration: 27 cos no (cos 0+a)20 for a > 1.

A: Note:- ∫C fz dz =2πi ×sum of residues cosnθ= Re ei nθ  cosθ=ei θ+e-i θ2      Given that  ∫02π…

Q: Use Green's Theorem to evaluate the integral |x?ydx + xydy where Cis the rectangle with vertices (0,…

A: To evaluate: The integral ∫Cx2ydx+xydy. Given information: The vertices of the rectangle is 0,0,…

Q: Apply Green's Theorem to evaluate the integral O(6y dx + 6x dy), where C is the triangle bounded by…

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Q: Prove that the area of the cardioid 3 r = a(1- cose) is , πα?. 2

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Q: Find the area shared by the circle r,= 10 and the cardioid r, = 10(1- cos 0). %3D

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Q: Use Green’s Theorem to evaluate ∮C squre toot of (1 + x^2)dx + 14x dy, where C is the triangle from…

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Q: 8K Use Green theorem to eva luate the . line integral : 3. 3 where c is ニ thecircle

A: Given the line integral

Q: Evaluate the contour integrals cosh z dz 4z2 + 72 z +1 dz 223 – 322 – 2z and around the unit circle…

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Q: Consider the non-right triangle below. у ст ZCAB T cm Suppose that m/CAB = of this triangle? 61°,…

A: Given,

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,…

Q: Use the Cauchy integral formulas to evaluate the eiz cos z dz, Yo z2(2z – 37) | where C is the…

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