exam1 - R . (b) Find the number b such that the line y = b...

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Name: Section Number: TA Name: Section Time: Math 20B. Midterm Exam 1 February 1, 2006 Turn of and put away your cell phone. No calculators or any other devices are allowed on this exam. You may use one page oF notes, but no books or other assistance on this exam. Read each question careFully, answer each question completely, and show all oF your work. Write your solutions clearly and legibly; no credit will be given For illegible solutions. IF any question is not clear, ask For clari±cation. 1. (6 points) Evaluate the following integrals. (a) Z 3 x sin( x 2 ) dx (b) Z 3 2 x 2 x - 2 dx # Score 1 2 3 4 5 Σ
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2. (8 points) Let R be the region enclosed by the curves y = x 2 and y = 4. (a) Find the area of the region
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Unformatted text preview: R . (b) Find the number b such that the line y = b divides the region R in part (a) into two regions with equal area. [Hint: Try integrating with respect to y rather than x .] 4 2 2-2 3. (6 points) Find the area enclosed by one loop of the polar curve r = 4 sin(2 ). 3 1 2 3 1 2 r = 4 sin(2t) 4. (6 points) Find the volume of a tetrahedron with height h and with a right triangular base with side lengths a and b . [Note: A tetrahedron is a pyramid with a triangular base.] h a b 5. (8 points) Let z = 1 + 3 i . (a) Write z in polar form. (b) Find z 10 and write it in standard ( a + bi ) form....
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This note was uploaded on 04/28/2008 for the course MATH MATH 20B taught by Professor Takeda during the Winter '07 term at UCSD.

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exam1 - R . (b) Find the number b such that the line y = b...

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