Find the diih of y integral tanar 230 e dn dy a) | shso b) c) O sysl-z 1-2 d) Nove of theoe

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: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: Fend the area of the regian that bes de the fest curve and de the second curve. 13cose cos

A: Given that, Two polar curves  We have to find the area of the shaded region. First, find the…

Q: The value of the triple integral 6zdV where E is the upper half E of the sphere of x² + y? + z? = 1…

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Q: evaluate the integral where c circle of positive rotation e^z/1 -cos(z) dz where C is |Z |= 1

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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: 5. Find the volume of liquid needed to fill a sphere of radius R to height h (Figure 18). R h…

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Q: Let C:z|=1 in the counterclockwise direction and I = $. dz, J = f. Lnzdz, and K = $. tanzdz. For…

A: We can apply cauchy Goursat theorem on I and K but not on J

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: 6. Use Green's Theorem to show that the area of the unit disk x2 + y? <1 in R? is T by evaluating a…

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t > 0. COS So r(t)dt Compute the integral above.

A: ∫0πr(t)dt=∫0π&lt;t,3cos t,3sin t&gt;dt               =∫0πtdt i+∫0π3cos tdt j+∫0π3sintdt k…

Q: The value of the integral (17 tan z- 17 sec r)dr = %3D O -68 O 4 O 68 O-4

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Q: ) USE THE METHOD OF VARIATON OF PARAMCTERS TO SULVE THE GIVEN ODE 8" +y'= secx Sec'x %3D

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Q: 22. Compute the contour integral (Баллов: 2) Sof (2) dz, z E C, if f (z) = and path is semicircle z…

A: Topic:- application of integration

Q: Use the given substitution to evaluate the integral.

A: Given integral: ∫sec22θ tan2θ dθ

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: | Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2, 1). Evaluate the…

A: ∫c y2xdx + 4yxdy=? We know that this form of integral is solved by Green theorem: ∮cP dx+Q…

Q: 19. z?e-l/? (a) |z| = 5 %3D

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Q: Let C be the arc of the circle |z| = 2 from z = 2 to z = 2i that lies in the first quadrant. Without…

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Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

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Q: Apply Green's Theorem to evaluate the integral P (4y² dx + 4x² dy) , where C is the triangle bounded…

A: See the details solution in below

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: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: Let C be the arc of the circle |z| = 2 from z = 2 to z = 2i that lies in Irant. Without evaluating…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Integrate f(z) = counterclockwise around the unit circle, usin %3D 28 – 9.7 - Cauchy's integral…

A: Given function is fz=1z8-9.7 and the contour is the unit circle oriented counterclockwise.

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

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: b) Evaluate the contour integral i ΙΣ where C {z : |z - i| = 3} and oriented counter clock-wise.

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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: sin(z) Sc (3z – 2)(z – 3) dz

A: Please find attachment for the

Q: Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is…

A: According to the given information, it is required to find the value of integral using Green’s…

Q: 21. (y² dx + x² dy)

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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: evaluate the contour integral z^2 -z^4/z-1)cos(z)where c:|z|=4

A: Introduction: Cauchy's integral formula is very significant in complex analysis. It helps to…

Q: Evaluate the integral [yda+zdy – rdz along the helix C given by - X = = cos πt, y = sin ít, z = t…

A: Line integration of the vector valued fumction

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: Evaluate the triple iterated integral. T/2 r cos é dr de dz Jo

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Q: to find the aren ruse 2) Use a polar integral enclosed by the three-petaled r = singe

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Q: Without evaluating the integral, show that z+4 67 -dz s 7. 2i +1 IC where C is the arc of the circle…

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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 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: Express R C Im(4iz + ¯z) dz where C is the directed line segment that joins the point −3 + 4i to the…

A: Consider the given integral which is required to solve.

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: What value of z in the interval 0< z< 2 corresponds to the greatest magnitude of Curl(F) where F(x,…

A: Given: F→(x,y,z)=tan(x),y4,2xcos(z-1)

Q: (Compute Sc (-3y+ony Sin(3))dxt (5x²-(ye)du Where C is a Simple Clased cUne in the plane oriented…

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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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