MA 242 Test 2 Last Name First Name Student ID Seat Code 1 1 points Show the basic definition theorems a 2D rectangular b Polar c 3D rectangular d Cylindrical e Spherical 1 2 1 points Carry out the following iterated integration Z 1 0 Z y 0 Z x 0 xz y dz dx dy 2 2 2 points RD x xy dA where D cid 8 x y x2 y2 2x 0 x y 0 cid 9 a Circle the economically best coordinate system slicing order from the following options 2D Rectangular 2D Polar dy dx dx dy d dr dr d b On the above plot of the domain do the followings i Write down equations in the chosen coordinate system describing the sides of the domain ii Draw generic slices illustrating the chosen slicing order iii Draw the extreme slices and label them c For each extreme slice determined the desired coordinate show the process in detail d Write down the resulting iterated integral 2 3 2 points RD x xy dA where D cid 8 x y y x 0 y x2 2 0 cid 9 a Circle the economically best coordinate system slicing order from the following options 2D Rectangular 2D Polar dy dx dx dy d dr dr d b On the above plot of the domain do the followings i Write down equations in the chosen coordinate system describing the sides of the domain ii Draw generic slices illustrating the chosen slicing order iii Draw the extreme slices and label them c For each extreme slice determined the desired coordinate show the process in detail d Write down the resulting iterated integral 3 4 3 points RD x yz dV where cid 8 x y z 1 x2 y2 z 0 z 0 x 0 y x 0 cid 9 a Circle the economically best coordinate system slicing order from the following options 3D Rectangular 3D Cylindrical 3D Spherical dy dx dz dx dz dy dz dr d dr dz d d d d d d d b On the above plot of the domain do the followings i Write down equations in the chosen coordinate system describing the sides of the domain ii Draw generic slices illustrating the chosen slicing order iii Draw the extreme slices and label them c For each extreme slice determined the desired coordinate show the process in detail d Write down the resulting iterated integral 4 5 3 points RD x yz dV where D cid 8 x y z x 0 z 0 y x 0 z y2 2y 0 cid 9 a Circle the economically best coordinate system slicing order from the following options 3D Rectangular 3D Cylindrical 3D Spherical dy dx dz dx dz dy dz dr d dr dz d d d d d d d b On the above plot of the domain do the followings i Write down equations in the chosen coordinate system describing the sides of the domain ii Draw generic slices illustrating the chosen slicing order iii Draw the extreme slices and label them c For each extreme slice determined the desired coordinate show the process in detail d Write down the resulting iterated integral 5 6 3 points RD x yz dV where D cid 8 x y z x 0 y 0 x2 y2 z2 0 x2 y2 z2 2z 0 cid 9 a Circle the economically best coordinate system slicing order from the following options 3D Rectangular 3D Cylindrical 3D Spherical dy dx dz dx dz dy dz dr d dr dz d d d d d d d b On the above plot of the domain do the followings i Write down equations in the chosen coordinate system describing the sides of the domain ii Draw generic slices illustrating the chosen slicing order iii Draw the extreme slices and label them c For each extreme slice determined the desired coordinate show the process in detail d Write down the resulting iterated integral 6
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