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.​​​

Find  and  for .

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Sketch the curve of the vector function r(t) = , t ≥ 0, and indicate the orientation of the curve.​

Find a vector function that represents the curve of intersection of the two surfaces:​the top half of the ellipsoid x2 + 6y2 + 6z2 = 36 and the parabolic cylinder y = x2.​