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

Q: Verify Green's Theorem by evaluating both integrals ƏM r dx + x² dy= dA ду Ne for the given path. C:…

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Q: Evaluate the integral. w2 In(w) dw

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Q: Evaluate the double integral 8xy dA, where D is the triangular region with vertices (0, 0), (1, 2),…

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Q: The particular integral of (De +1)y= cosx is O None of the choices zsinz 2 ICOSI 2 ECOSI 2 O zsinz 2

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Q: w In w dw

A: There is a function given and we have to integrate it. F=∫w.lnwdw

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: Find the value(s) of c such that the area of the region 2 bounded by the parabolae y = x² – c² and y…

A: see below the answer

Q: Evaluate the integral / cos[3 +1/(z – 3)] dz, where Y is the unit square with corners at 0, 1, 1+i e…

A: Given; ∫γcos3+1z-3dz Where, γ is the unit square with corners at 0,1,1+i e i

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: Let G(u, v) = (, uv). Use the Change of Variables Formula to compute the area of the image of [1, 4]…

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Q: Verify Green's Theorem by evaluating both integrals aN y? dx + x² dy = /, J da ay ax for the given…

A: We have to verify the green theorem for the

Q: Evaluate [[r'dr de over the area bounded between the circler = 2 cos@ and r= 4 cos -41π/2 O -43π/2 O…

A: Given: ∬r3drdθ over the area between the circle r=2cosθ and r=4cosθ To find the limits of r and θ…

Q: Evaluate the integral:S csc?xv1+ 3cotx dx. A. 등(1+3cotx) + c B. -(1+3cotx) + c c. (1+3cotx) + c…

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Q: Find the area +6 C1 R -6 +6 C2: 4x2 + y² = 16 -6 using green's theorem.

A: We are given the above region of which we need to find the area and as per the instruction, we need…

Q: Find the sum of the residues of f (z) = sin z at its poles inside the circle |z| = 2. z cos z

A: Residue theorem∮f(z)dz=2πi(R1+R2+.........Rn)             =2πi(sum of the residues at the poles…

Q: Use symmetry to evaluate the given integral. (7 Зх + 2y) dA, - where D is the region bounded by the…

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Q: Verify Green's Theorem by evaluating both integrals aN v? dx + x² dy | dA ду ax for the given path.…

A: Given problem:-

Q: Which integral represents the area of R? Choose 1 answer: 3π A 16³ (²1 + 2 cos² (0) + 2 cos¹ (0)) de…

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Q: Verify Green's Theorem by evaluating both integrals v? dx + x? dy = . dA дх ду for the given path.…

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Q: Find all Integers a so that the area enclosed by the lines y=ax,y=0 and x + 2y-4=0 is a natural…

A: To find: All integers a so that area enclosed by the lines y=ax, y=0, and x + 2y-4=0 is a natural…

Q: Find the product of the integral 1- S x²cos(xy)dxdy

A: We have to change order of integration first.

Q: Evaluate the double integral || 8xy dA, where D is the triangular region with vertices (0, 0), (1,…

A: Given data: The first vertex is O=(0, 0). The second vertex is B=(1, 2). The third vertex is A=(0,…

Q: show the steps of this integral: | dxp In p = In a H

A: Given that H=-∫0adxρlnρ This can be written as, H=∫0a1ρdρ

Q: Verify Green's Theorem by evaluating both integrals aN dA Lv? dx + x² dy = ду ax for the given path.…

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Q: Verify Green's Theorem by evaluating both integrals AN fx2ax+x²&y-LI (x-an) = y2 dx + x2 dy dA ?х ду…

A: We can solve as follows

Q: Use areas to evaluate the integral. 11b 2s ds, 0<a<b

A: Consider the integrals, ∫a11b2s  ds,   0&lt;a&lt;b

Q: Find the areas of the regions Inside one loop of the lemniscate r2 = 4 sin 2θ

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Q: Evaluate the following integral JI (1 – (x + y))dA where T is the triangle with vertices (0, 0), (1,…

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

A: Given-A circle C,which is unit circle enclosing the origin           -f(z)=zz  To find- ∮Cf(z)dz

Q: Compute the given integral. rp: +C

A: Please refer the attached image for complete solution

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

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Q: Compute the contour integral dz, where l'is the contour of the perimeter of the square with vertices…

A: We will do it  by dividing r into 4 paths.

Q: Evaluate the given line integral. (y, -x) · dR, where C consists of the uppder part of 2² + y? = 1…

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Q: 1 ydx 2 5 (wdy – ydr). P = xdy - C C

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Q: Verify Green's Theorem by evaluating both integrals v? dx + x2 dy dA ax for the given path. C:…

A: 9

Q: Can i get help step by step with this problem?

A: Given:

Q: Consider the following integral A suitalle trigonometoc sulstitulion to leduce lt to a simpler…

A: Answer

Q: 5. Evaluate the integral fffn 7 dzdydr, where R is the region enclosed by ² + y? 2 = Zz²+y² .

A: To convert the cartesian plane into cylindrical coordinates, Put and

Q: ir a unit circle centered at 7=1) (2 -17

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Q: T/3 L, S, Srª yz tan xdxdzdy

A: follow the  next step

Q: which of the sets is orthvoonal under the given inner product on C[0, T] ? = S fusgıx) dx I. {1,…

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Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1

Q: z is a complex variable z=x+iy pic attached with question

A: To establish the analycity of the  function under the given conditions.

Q: Prove,J w' Sin wx du %3D COSZ 2

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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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