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# MULTIDIMENSIONAL CAL MATH 2057

LSU

GPA 3.72

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This 1 page Class Notes was uploaded by Madison Gottlieb Sr. on Tuesday October 13, 2015. The Class Notes belongs to MATH 2057 at Louisiana State University taught by R. Estrada in Fall. Since its upload, it has received 38 views. For similar materials see /class/222629/math-2057-louisiana-state-university in Mathematics (M) at Louisiana State University.

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Date Created: 10/13/15

Practice for Test III 1 Find m y2 223 d5 where C is the curve z 5t y 12cos t z 12sint 0 S t 27139CAlSO nd the length of this curve 2 Find y 2 dm x 2 dy z 7 3 dz where 0 consists of the segments from 005 toC128 and from 128 to 328 3 Find a function f such that Vf F 1 2zy ln 2 i x2 2yj and use this to evaluate the integral CF ClI39 along the path 0 z 2 t3 y t2 sin m 0 S t S 1 4 Use Green7s theorem to evaluate the line integral xsy 7 x4 dm xyz yg dy where C is the rectangle with vertices 11 21 27 30 and 13 5 Use Green7s theorem to nd the area of the region bounded by the curve with para metric equations z t 7 t2 y t 7 t3 0 S t S 1 6 Find the area of the surface 2 the part of the graph of the paraboloid z 2x2 2y2 below the plane 2 50 7 Determine Whether or not the eld F yum1i zzewyz zj zyemyz y 2zk is conservative if so nd f with Vf F 8 Set up the double integral needed to compute the surface integral 2 zyzzg dS where E is the part of the graph 2 2 7 y3 above the region 0 g x S 3 2 S y g 5 9 Set up the double integral needed to compute the surface integral EFxyz9 where F zy z y2 z i 2 zj 2 y k and E is the surface obtained by rotating the graph of y sin x 0 S x S 7139 around the z7axis 10 Find the integral of 9 by using the divergence theorem 11 Find using Stokes7 theorem the integral curlFzyz d 2 where F zy z y2i22j2k and where E is the hemisphere z2y222 1 z 2 0

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