1. Find the surface area of the paraboloid z = 4 – a² – y², for z > 1 using the formula 2 dz A(S) = + dy +1dA.

Q: . Evaluate (x² + y) dv G if G is the solid bounded by the parabolic cylinder z = y², xy-plane and…

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Q: Evaluate fff 1- x2 - y2-z2 dx dy dz where V is the volume of the sphere x? + y? + z2 = a? by…

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Q: 4. A 3D solid has base that sits in the x-y coordinate plane. That base is a triangle with vertices…

A: Integrating the equation of curve under certain limit gives the value of area between curve and axis…

Q: Find the surface area generated by rotating the semi-circle x = 49 – y? be- tween -7 < y 7 about the…

A: Given, x=49-y2  between -7≤y≤7 dxdy=1249-y2-2y=-y49-y2 By the formula:  S=∫2πx1+dxdy2 Plug the…

Q: a) Find the surface area of the object obtained by rotating x = e2y , –1 <y <1 about the y – axis.

A: We have to find the surface area of the solid obtained by rotating the curve x=e2y about the y-…

Q: Use cylindrical coordinates to evaluate the triple integral √² + y²dV, where E' is the solid bounded…

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Q: 2. Integrate f(x, y) = sin /x2 + y² А. over the closed unit disk.

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