3. The centroid (#, 9) of an area D can be calculated by To dA To dA (a) Use Green's Theorem to show 1dy 2A Je where A is the area of D. (b) Use part (a) to calculate the centroid of a quarter circle with radius 1.

Q: tegral by transforming to polar coordinates.

A:

Q: Find the area of the surface generated by revolving the curve about they-axis. y=81-x²,05x59 A B…

A: Given :y=81-x20≤x≤9

Q: Find the formula of the area of ellipse using calculus integrals

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Q: QI) Evaluate the integral dy dx using polar coordinate

A:

Q: 4. Evaluate √² +² dzdy by changing to polar coordinates. Sketch the region of integration..

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Q: Use Green's theorem to find the area between ellipse 16 = 1 and circle x2 + y2 = 25.

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Q: 27T (2 .. Polar foum>Al8) = 1+ 90ucose 924 go esine t dedo 431

A: For the double integral, ∫ab∫cdf(x,y) dx dy, the limits of integrations for the variables x, y can…

Q: Q4) Find plane area inside polar function r = 2 and outside polar function r = -2sine in third…

A:

Q: Length is 3x − 4, area is 6x^4 − 8x^3 + 9x^2 − 9x – 4

A: On solving this we will get

Q: Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.

A: Using Cartesian coordinates to polar coordinates.

Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

Q: Sez dz along the line segment from 0 to 1+ in/2.

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Q: r= sin E-0) in first quarter.

A: