Find the volume of the given solid.​Under the paraboloid and above the rectangle .

Evaluate the double integral , where R is the region bounded by the graphs of y = (x – 1)2 and y = –x + 3.

Calculate the iterated integral. Round your answer to two decimal places.​​

Find the volume of the solid bounded in the first octanat bounded by the cylinder z = 9 – y2 and the planes ​x​ = 1.

Find the average value of f over the given rectangle. ,

Use the Midpoint Rule for double integrals with to estimate the volume of the solid. Round your answer to three decimal places.​

Sketch the curve of the vector function r(t) = 2sinti + 5costj, and indicate the orientation of the curve.

Find the domain of the vector function r(t) = 8ti + j.​

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Find the derivative of the vector function.​​​