21B-WQ082 - 21B Calculus, Sections A01-A05 Final Name: ID:...

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Unformatted text preview: 21B Calculus, Sections A01-A05 Final Name: ID: Section: 1. (5 points) Evaluate the improper Integral Z x 2 e- 3 x dx 2. (5 points) Evaluate Z 2 cos(2 x ) sin( x ) dx Name: ID: Section: 2 3. (5 points) Evaluate the indefinite integral Z 2 x- 4 x 2- x dx 4. (5 points) Z x 3 p 4- x 2 dx Name: ID: Section: 3 5. (5 points) Evaluate the definite integral Z 4 1 t ln( t ) dt 6. (5 points) Evaluate the indefinite integral. Z sec 2 tan 9- tan 2 d Name: ID: Section: 4 7. (10 points) Find the centroid of the triangle bounded by the lines y = 6 x , y = 6, y = x . Name: ID: Section: 5 8. (20 points) Let f ( x ) be a continuous function which satisfies Z ln( y ) 2 f ( x ) dx = y 3 + C What does C have to be in order to even make this equation solvable? Solve for f ( x ). Clearly explain your answer. Name: ID: Section: 6 9. (20 points) This is a multi-part question. First find the volume of the unbounded solid generated by rotating the curve y = x- 2 from x = 1 to x = a, a > 1 about the x-axis. Second, find the volume of the solid1 about the x-axis....
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This note was uploaded on 05/19/2009 for the course MATH 21B taught by Professor Vershynin during the Spring '08 term at UC Davis.

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21B-WQ082 - 21B Calculus, Sections A01-A05 Final Name: ID:...

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