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1. Evaluate triple integrals. sinx sin y dzdydx (a)Jo So (b) o JoV dz dxdy
sin y 11. Evaluate the integrals Sysin xy dxdy and sketch the corresponding 0 0 region. (10pc
MAT233 Final Exam Summer 2019 /1-z2 1 o 8. Evaluate Jo Jo Joz z sin x dy dz dx
MAT233 Final Exam Summer 2019 /1-z2 1 o 8. Evaluate Jo Jo Joz z sin x dy dz dx
Evaluate the integral cosh(r)dx dy dz Jo o
Evaluate the integral cosh(r)dx dy dz Jo o
1. Evaluate the following integrals by transforming them to polar form (3r + 2y2)dydr, (2 +y)dydr, (r2 -)dydr, 22ydr o Jo (23y) dydr, 2 3y) dydr,
1. Evaluate the following integrals by transforming them to polar form (3r + 2y2)dydr, (2 +y)dydr, (r2 -)dydr, 22ydr o Jo (23y) dydr, 2 3y) dydr,
DO
NOT use a calculator. Exact answers only, no decimals.
1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr
1. (10 pt each) Evaluate the following integrals: since) dz In(In(x b. dr c. cos(x)(sin(a)2 dz d.2tan (') dr
1. Evaluate the integrals: (a) S (x2 - y²)dz, where is the straight line from 0 to i. (b) e dz, where y is the circle of radius 1 centered at 2 traveled counterclockwise.
16. o integrad [**** The triple da dy dz describes the solid pictured at right. Rewrite as an equivalent triple integral in the following orders (DO NOT EVALUATE): 31 (a) dy dz dx (b) du dz dy 2. 16-2 21. Given dy da, 16- (a) Sketch the region of integration and write an equivalent iterated integral in the order dx dy. (You do not need to evaluate it!) (b) Now write it as an equivalent iterated integral in polar coordinates....
4. Rewrite the following triple integral so that the order of integration is dy dx dz. Do not evaluate it. (3x + y) dz dy dit
The question is, evaluate the following integral.
1+x2+22 43. dy dx dz Jo Jo
I sinta fosinta 3. (40 points) Evaluate the following integrals: (a) (10 points) sin(2 + 7)dz, where C is the square with vertices at 2i, 3i, 1+ 3i and 1+2i, in this order. (b) (10 points) sin(22) $c 2+1 where C is the positively oriented (counter-clockwise) triangle with vertices (0,0), (2,0) and (0,5). (c) (10 points) cosh(22) -dz, (3-2) where is the negatively oriented (clockwise) circle centered at (1,1) of radius 2. (d) (10 points) dz, 2-1 where C consist...