EX4: Evaluate the integrals using polar coordinates SSR ex²+y² Where R is semicircular region bounded by the x-axis and the curve y = √1-x² y-VI-²

Q: Q4. : Find the area of the region R enclosed by the curve y=x+2. Y3DX2 and the line

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Q: Find a parametrization of the curve ²/3 + y²/3 = 1 and use it to compute the area of the interior.

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Q: The area of the surface obtained by rotating the curve y = x2, 0sxs1 about the y-axis is

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Q: 1 Find the area of the surface obtained by rotating the curve y = In(1 – x²), 0 < x <. about the

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Q: Find the Area of the Surface obtained by rotating the curve about the y -axis y = √√x, 1 ≤ y ≤2

A: Given y=x13    1≤y≤2Rotating about y-axisarea of surface of revolution about tghe y…

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

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Q: Find the area of the surface S defined by z = xy and x² + y² ≤ 3. (Use syntax like 2*pi/3)

A: (.)  Given ,  Area of the surface S defined by z=xy and x2+y2≤3 .   If  z=f(x,y) ∀ (x,y)∈R  the…

Q: Find the area of the region enclosed by y = 5x – x and y = x Refer: Area between Curves O 12/5 O…

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Q: Find the area of the surface obtained by rotating the curve y = x about y-axis for 1< y< 3.

A: We have to find surface area

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: Make two separate plots of the function z - 2 sin (1.5x) in the domain -3sxs3 and -3Sys3. 3-D…

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Q: Find the area of the surface obtained by rotating the curve y = √5x from x = 0 to = 4 about the…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: What is the moment of inertia of this area about the line y = -10 ?

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