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Quiz 3 for Math 140-01, Spring 2006, Quizzes of Mathematics

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.

Typology: Quizzes

Pre 2010

Uploaded on 08/30/2009

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Math 140-01
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.
1.(3 pts) If F0(x) = G0(x), what is F(x)G(x) equal to?
2.(14 pts) Evaluate the following:
(a) Z9
x3e0.4xdx
(b) Z2y1/2
3y2
ydy
3.(4 pts) Use geometry to evaluate Z0
4
16 x2dx. Hint: Draw the region.
pf3
pf4

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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).