-(/2/2)+sine -1/4 (/2/2)+sin0 27. 2 r dr de – 2 r dr de -1/4 -1/2 -2л /3 с(1/2)+сos@ 47/3 (1/2)+cos e 28. 2 r dr do – 2 r dr de 0.

Q: 3 LL -3√√√9-x² Jo √9-x²-y² (x² + y² + z²) dz dy dx

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Q: Use Green's Theorem to evaluate the following line integral. Of dy -g dx, where (f,g) = (7x,11y) and…

A: Use Green's Theorem to evaluate the following line integral.

Q: 11. Evaluate the following integral by converting it into polar coordinates. || 2xydA, D is the…

A: 1st we write the eq. of the circle  r1 = 2, r2 = 5

Q: evaluate the double integral SRS f(r, 0) dA and sketch the region R.

A:

Q: 3) Evaluate the iterated integral by converting the to polar coordinates -√₂x-x² a) √²ty² dydx…

A: Given that, The integrated integral: (a) ∫02∫02x-x2x2+y2dydx,  such that , the region is…

Q: Let C be a simple closed contour |z-2|=3 . Use the extension of Cauchy Integral Formula to evaluate…

A: Given that  Mod(z-3)=3  By using Cauchy integral formula, the solution is as below

Q: A6] Evaluate the integral J: J over the area of a circle of radius 2, using polar coordinates.

A: We have, J=∫∫Ax2y2dxdy   Equation of circle is, x2+y2=22   In polar coordinates, x=rcosθy=rsinθ Here…

Q: Evaluate the integral de. f(0) = Lo sinh 0 – a %3D “ OP- where a is a complex number (Im a + 0.)

A: Given function is  f(θ)=∫-∞∞θsinhθ-adθ or we can write it as f(x)=∫-∞∞xsinhx-adx     (1) since…

Q: Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle…

A:

Q: Sketch the following region R. Then express || f(r,0)dA as an iterated integral over R. R The region…

A:

Q: Write the sum of the two iterated integrals as a single iterated integral by converting to polar…

A:

Q: Convert the integral 1-22 4-a-y? I = z dzdydr into an integral in spherical coordinates.

A: Cartesian to spherical coordinate:

Q: Use a double integral in polar coordinates to find the area of the region described. Theregion…

A:

Q: Set-up the integral which yields the area of the indicated region R between C1 and C2. Given: polar…

A: Solution:-

Q: In polar coordinates, which of the following double integrals has bounds that represents the region…

A:

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly.…

A:

Q: 344. Use Stokes' theorem to evaluate line integral (zdx + xdy + ydz) , where C is a triangle with…

A:

Q: Convert the following iterated integrals (SET UP ONLY): x² a.) [f dA from Cartesian coordinates to…

A: The simple change polar coordinate...

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 51…

A:

Q: 2.Use a double integral to find the area of the region. a. The region enclosed by tje cardioid r =1…

A: We have to use double integration to find the area of the region.

Q: Sketch the following region R. Then express | f(r,0)dA as an iterated integral over R. R The region…

A: This question is related to area bounded by curves, We will solve it using given information.

Q: Each of the integrals or integral expressions in Exercises 21–22 represents the area of a region in…

A: 21. Consider ∫02π∫01+ sin θrdr dθ = ∫02πr2201+sin θ dθ  =∫02π1+sin θ2-022 dθ =∫02π1+sin θ22 dθ…

Q: e region N= {(x, y) e R² : x > 0, y > x, x² + y² < 1}.

A:

Q: Convert the given iterated integrals (SET UP ONLY): dA R Vx² + y² a.) from Cartesian coordinates to…

A:

Q: 3. Apply Cauchy integral formula to find the value of the integral: sinz Se where C:|z| =÷. Also…

A: Use Cauchy integral formula and residue theorem.

Q: The double integral I = S Vx²+y² dydx in polar coordintes is: the double integral None of these

A: We know that : x=rcosθand,y=rsinθ Therefore, x2+y2=r2cos2θ+sin2θ=r2⇒r=x2+y2.

Q: 5. Use a double integral in polar coordinates to find the area inside the graph of r = 2cos0 and…

A: Givenr=2cosθ and r=1⇒2cosθ=1⇒cosθ=12⇒θ=-π3,π3

Q: Calculate using polar double integration the area of the region that lies between the circles r-…

A:

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 7 149-x2 dy dx - 7…

A:

Q: 2)use the polar coordinates to evaluate the double integral: A) B) y dA R is bounded by r= 2-cose

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Q: Use a double integral in polar coordinates to find the region described: The region in the first…

A:

Q: 1 5-y3 x + y dædy

A: The given integral ∫01∫y5-y3x+ydxdyis in the cartesian co-ordinate where y≤x≤5-y3  and 0≤y≤1we have…

Q: Sketch the region of integration and convert the polar sum of integrals to a Cartesian integral or…

A:

Q: 2-.Change the Cartesian integral into an equivalent Polar integral then evaluate the polar integral.…

A:

Q: Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle…

A: By Green's theorem, ∫CPdx+Qdy=∬DQx-PydA. Here the integral is  ∫Csin 5y dx+5y dy and the region is…

Q: 6) Find the centroids of the shaded region. Indicate the typical rectangles and derive the values…

A: As you post multiple questions  I only answered first one

Q: 11. Evaluate the following integral by converting it into polar coordinates. |/ 2rydA, D is the…

A:

Q: 10. Use polar coordinates to evaluate the integral -s* drdy D= {(r, y) € Rlz² + y² > 9}

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Q: Write the sum of the two iterated integrals as a single iterated integral by converting to polar…

A: A detailed solution is given below.

Q: Evaluate the double integral / F(r, ®) dA. "* (3 cos(8) r dr de Sketch the region R. 7/2 A/2 2 1 2…

A: To evaluate the given double integral: ∫0π∫03 cos θr dr dθ

Q: Change the Cartesian integral to an equivalent polar integral, and then evaluate. 1 dy dx - 5 25-x2…

A: Option (B) is the correct choice.

Q: w/2 x cos cos z dy dx dz

A:

Q: Convert the given iterated integrals (SET UP ONLY): x2 dA + y2 (a) from Cartesian coordinates to…

A:

Q: Evaluate the double integarl sin(x2 + y2)dA using polar coordinates, where R is the region between…

A: Please rate and feel free to ask any query about any part of the question.

Q: 29-32 Use double integration to find the area of the plane re- gion enclosed by the given curves.…

A: Solution is in step 2

Q: Sketch the region of integration and convert the polar sum of integrals to a Cartesian integral or…

A: Here is the solution of the given problem.

Q: 3. Evaluate the iterated integral by converting to polar coordinates : (22 + y?)dydr

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Q: Choose the correct integral in polar coordinates to evaluate 1 2 2 the integral 0, 12x-* 2x-x…

A: Consider the given integral

Q: Evaluate the spherical coordinate integrals in Exercises 43-48. -п р2 sin ф 43. p' sin ф dp dф dө ГC…

A: