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21B-WQ082

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

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21B Calculus, Sections A01-A05 Final Name: ID: Section: 1. (5 points) Evaluate the improper Integral 0 x 2 e - 3 x dx 2. (5 points) Evaluate 2 π 0 cos(2 x ) sin( x ) dx

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Name: ID: Section: 2 3. (5 points) Evaluate the indefinite integral 2 x - 4 x 2 - x dx 4. (5 points) x 3 4 - x 2 dx
Name: ID: Section: 3 5. (5 points) Evaluate the definite integral 4 1 t ln( t ) dt 6. (5 points) Evaluate the indefinite integral. sec 2 θ tan θ 9 - tan 2 θ

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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 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.

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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 solid generated by rotating the same curve about the y-axis. Now take the limit as a → ∞ . Compare the two results and discuss.
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21B-WQ082 - 21B Calculus Sections A01-A05 Final Name ID...

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