Write a triple integral in cylindrical coordinates of the function f(x, y) = x+y over the region bounded by the xy-plane, z = 20 - 3x² - 3y2, and z= x² + y².

Q: Use cylindrical coordinates to calculate the integral of the function f(x, y, z) = z over the region…

A: Given: fx, y, z=z We have to calculate the integral of the given function over the region above the…

Q: Evaluate the triple integral in rectangular coordinates x=2 y=√√4-x² z=2 L x=-2y=-√4-x² z=√x²+ y²…

A: To evaluate the given triple integral∫x=−2x=2​∫y=−4−x2​y=4−x2​​∫z=x2+y2​z=2​(x2+y2)dzdydxusing…

Q: At what point on the ellipsoid x² + y² + 9z² = 1 is the tangent plane parallel to the plane x + 2y +…

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Q: Find the volume of the solid whose base is the region in the xy-plane that is bounded by the…

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Q: Evaluate the surface integral. y dS, S is the helicoid with vector equation r(u, v) = (u cos(v), u…

A: Consider the provided question,

Q: Converting into cylindrical coordinates the integral r9-(x²+y²) 9-a2 ydzdrde 9-x2

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Q: Find the centroid (, y) of the region bounded by: y = 2x² + 2x, y = 0, and x = 9 y=

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Q: termine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octan

A: The given solid is bounded by the surface 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

Q: There is a curve parametrized by x = 3t, y = 2t°, 0<t an equation for this curve in terms of ne…

A: Here we have,

Q: Find the Centroid for the lamina created between the functions y=x and y=x2

A: Given that  Functions y=x and y=x^2  To find the Centroid for the lamina created between the…

Q: Integrate the function (x² + y²) over the region E that is bounded by the xy plane below and above…

A: Evaluation of triple integrals using cylindrical coordinates