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Method of Substitution - Calculus Two for Biological Sciences - Exam, Exams of Calculus

This is the Exam of Calculus Two for Biological Sciences which includes Numerical Sum, Approximation, Midpoint Rule, Terms, Modeled, Type Equilibrium Points, Starting Population etc. Key important points are: Method of Substitution, Explanation, Constant, Definite Integral, Substitution, Exact Value, Mathematical Tables, Formula and Substitution, Problems, Concise Solution

Typology: Exams

2012/2013

Uploaded on 02/18/2013

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Math 30: Unit 1 Exam
Fall Semester 2006
Instructions. Read each problem carefully and follow all of its instructions. For each
of the problems below, write a clear and concise solution in your blue book. For any
short answer questions, write clearly your answer and any additional explanation that is
needed.
1. (5 points) Explain why you must add a constant when computing an indefinite in-
tegral, but not when computing a definite integral.
2. (5 points) Evaluate exactly the integral Z2
1
x2+1
xdx.
3. (5 points) Use the method of substitution to find Zzsin(z2+1)dz
4. (5 points) Find the exact value of Z1
04te2tdt.
5. (5 points) According to a book of mathematical tables,
Z1
1+u2du=arctan(u) + C.
Use this formula and substitution with u=exto find
Zex
1+e2xdx.

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Math 30: Unit 1 Exam

Fall Semester 2006

Instructions. Read each problem carefully and follow all of its instructions. For each of the problems below, write a clear and concise solution in your blue book. For any short answer questions, write clearly your answer and any additional explanation that is needed.

  1. (5 points) Explain why you must add a constant when computing an indefinite in- tegral, but not when computing a definite integral.
  2. (5 points) Evaluate exactly the integral

∫ (^2)

1

x^2 + 1 x

d x.

  1. (5 points) Use the method of substitution to find

z sin( z^2 + 1 )d z

  1. (5 points) Find the exact value of

∫ (^1)

0

4 te^2 t d t.

  1. (5 points) According to a book of mathematical tables, ∫ 1 1 + u^2

d u = arctan( u ) + C.

Use this formula and substitution with u = ex^ to find ∫ (^) ex

1 + e^2 x^

d x.