Integration & Accumulation of Change unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Improper: infinite integrand
Improper integral with an infinite limit
p-integral at infinity
At infinity shrink fast, near zero blow up slowly
FTC Part 2 with a chain rule
Integral of a constant
Interpreting an integral in context
Trapezoid and concavity
Unequal widths are normal
Integration by parts returning the original
Technique decision order
Midpoint runs opposite the trapezoid
Short answer 1. Define or explain: Why LIATE works
3 ptsShort answer 2. Define or explain: Trigonometric substitution qualitatively
3 ptsShort answer 3. Define or explain: Solving for A and B fastest
3 ptsShort answer 4. Define or explain: Never substitute ∞
3 ptsFree response
9 ptsNO CALCULATOR. The rate at which cars enter a parking garage is modeled by the function E, and the rate at which they leave is modeled by L. Both rates are measured in cars per hour, and selected values are given in the table. At time t = 0 there are 60 cars in the garage. t (hours) 0 2 5 8 12 E(t) 30 48 52 36 18 L(t) 10 22 40 54 30
A. Use a left Riemann sum with the four subintervals indicated by the table to approximate ∫₀¹² E(t) dt. Using correct units, interpret the meaning of this integral in the context of the problem.
B. Use the data to approximate E′(6.5). Show the computations that lead to your answer, and indicate units of measure.
C. Based on the data, is there a time t in the interval 5 < t < 8 at which the number of cars in the garage is neither increasing nor decreasing? Justify your answer.
D. Using a right Riemann sum with the four subintervals indicated by the table, approximate the number of cars in the garage at time t = 12.