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A math quiz for a college-level calculus course. It includes instructions, directions, and problems for students to solve. The quiz covers topics such as differentiation, integration, and geometry. Students are required to show their work and use proper notation. The document also includes a bonus question about drug kinetics.
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Math 140- Quiz 3 Spring 2006
Name: ID: Date:
Directions: Show all work. No work equals no credit. You may use a basic scientific calculator, but no graphing calculators. Use proper notation. The use of pen will also result in a score of zero.
(3 pts) 1. If F ′(x) = G′(x), what is F (x) − G(x) equal to?
(14 pts) 2. Evaluate the following:
(a)
x
− 3 e−^0.^4 x
) dx
(b)
∫ (^2) y 1 / (^2) − 3 y 2
y
dy
(4 pts) 3. Use geometry to evaluate
∫ (^0)
− 4
16 − x^2 dx. Hint: Draw the region.
(12 pts) 4. Evaluate the following:
(a)
∫ (1 − t)e^2 t−t
2 dt
(b)
∫ (^) t (^2) + 2
t^3 + 6t + 3
dt
(12 pts) 5. Evaluate the following:
(a)
∫ (^2)
0
(5x^2 − 4 x + 2) dx
(b)
∫ (^0)
− 1
y(2y^2 − 3)^3 dy
Bonus: 5 pts In the model of drug use, the concentration of a drug in a user’s bloodstream is given by
C(t) = e−kt
∫ (^) t
0
Deky^ dy (1)
where k is a constant (rate of drug removal), D is a constant (rate of drug introduction). Integrate to find C(t).
