MA 227 , Calculus - III. Test - III Wednesday, December 3, 2003.
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.(Please, print)
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Calculus III - Test 3: Integration and Center of Mass, Exams of Advanced Calculus
The test questions for ma 227 calculus iii. The test covers various topics including integration, polar coordinates, center of mass, and solid regions. Students are required to evaluate integrals, find volumes, and calculate centers of mass. Reasoning and justification of answers are required.
Typology: Exams
2012/2013
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MA 227 , Calculus - III. Test - III Wednesday, December 3, 2003.
. Student’s Name (Please, print)
GIVE REASONS FOR YOUR ANSWERS!
TEST 3:
HW:
The Final Grade for TEST 3: I. (20 %) Evaluate the integral: ∫ D^ (x^ −^2 y)dA, where D is the region bounded by the line x = y and the parabola y = x^2.
III. (20 %) Find the center of mass of the thin plate with density 3 bounded by lines x = 0, y = 1 and the parabola y = x (^2) in the first quadrant.
IV. (20%) Find (^) ∫ E
∫ ∫ x dV,
where E is a solid tetrahedron bounded by the planes x = 0, y = 0, z = 0 and 2 x + y + z = 4 in the positive octant.