This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 21B Calculus, Sections A01A05 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 multipart 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 xaxis. Second, find the volume of the solid1 about the xaxis....
View
Full
Document
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.
 Spring '08
 Vershynin

Click to edit the document details