3) Evaluate the double integral S,(x² + y²) dxdy using polar coordinates, where region Ris the semi-circle as given by shaded region in Figure. R (-2,0) (2.0) 4) Let f(x, y) = x + y be the density of a distribution of a mass over a triangular region R with vertices (0, 0), ( 0, 1), and ( 1, 1). Find the total mass.

Q: The surface S is the portion of the plane z=y+3 that lise inside the cylindrical region x2+y2<=1…

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Q: Use Stokes' Theorem to evaluate (integral) F (dot) dr. C is oriented counterclockwise as viewd from…

A: here we will use stokes theorem for any vector field F  ∫CF.dr=∫∫S curlF dS where C is a positively…

Q: Double integral: Find the volume V of the solid above the polar rectangle R = (1) {(r,8)}:1 <r s 3,0…

A: The volume of the solid using the double integral can be calculated by the formula . Here, Did the…

Q: fof 8 6 5 1 3 2 5.6 8 9 10 1 Find the centroid of the region displayed in the graph. (x, y) =

A: We have to find the centroid of the shaded region:

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2…

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Q: 17. Given p(x,y,z) = xyz + 5, find the surface integral of the normal component of grad o over x² +…

A: ϕx , y , z=xyz+5. To Find: Surface integral of the normal component of gradϕ over x2+y2+z2=9.

Q: Find the centroid x, y, z of the region R cut out of the region 0 < z< 8/x² + y² by the cylinder x2…

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Q: 1.8 Consider the double integral VP 12 + y? ry where R is the region of the XY plane, given in the…

A: As per guidelines we experts are allowed to solve one problem at a time. please reupload the second…

Q: sketch! Convert to polar coordin is the region in the first quadrant enclos

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Q: 1) Find the vohume of the region bounded by the Z = 2 - 4x2 - 4y² and the plane Z-0 (Note : Use…

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Q: Q9/ Find the centroid of the region enclosed by the cardioid r = 1 + cos 0.

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Q: Find the Integral Centroid of Plane Area Under a Curve

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Q: Use stokes Theorem  Calculate the total effect of the wind (W(x,y,z) = along the path P =…

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Q: Let T be the triangular region region with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1) oriented…

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Q: 2. Find the centroid of the region R = {(x,y): x ≥ y²/2, x ≤ y}.

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Q: Ex,y) de by dividing the rectangle R with vertices (0, 0), (4,0), (4, 23, and (0, 2) into eight…

A: The image of rectangle can be drawn with the given coordinates.

Q: Use polar coordinates to describe the region shown. y 10 5 -10 -5 10 5 -10 R = {(r, 8): 0 srs 3…

A: Here we will use some points and shape of given graph to decide which equation representing it .