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Midterm 1 Exam Review: Integration and Differential Equations - Prof. Qinglan Xia, Exams of Calculus

University of California - DavisCalculus
Prof. Qinglan Xia

A review for an upcoming midterm exam focusing on integration techniques, including antiderivatives, indefinite integrals, definite integrals, and the substitution rule. Additionally, it covers solving differential equations and calculating areas between curves. Students are encouraged to use resources such as previous exams, homework, lecture notes, and textbooks for preparation.

Typology: Exams

Pre 2010

Uploaded on 07/30/2009

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Review for Midterm 1
Information for Midterm 1:
•Where: Here in this classroom.
•When: This Friday (October 17,2008), on lecture time 12:10–1:00pm .
•Who: You, of course.
•What: Contents of Section 4.8 and Chapter 5.
This is a closed book/notes/friends exam. Totally 4 pages, 6 problems. No calculator is allowed.
A previous exam for the last year has been posted on the course webpage. You are encouraged to take it first, and then compare
your answers with the provided solutions.
Helpful resources:
•This Review
•Previous Exam (posted on the course webpage)
•Homework; In particular, PAPER HOMEWORK!
•Lecture Notes
•Textbook
•Online learning materials.
Some basic concepts/methods/theorems
•Antiderivatives; Indefinite integral
•Initial value problem;
•Partition of an interval and the norm of a partition;
pf3
pf4

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Download Midterm 1 Exam Review: Integration and Differential Equations - Prof. Qinglan Xia and more Exams Calculus in PDF only on Docsity!

Review for Midterm 1 Information for Midterm 1:

  • Where: Here in this classroom.
  • When: This Friday (October 17,2008), on lecture time 12:10–1:00pm.
  • Who: You, of course.
  • What: Contents of Section 4.8 and Chapter 5.

This is a closed book/notes/friends exam. Totally 4 pages, 6 problems. No calculator is allowed. A previous exam for the last year has been posted on the course webpage. You are encouraged to take it first, and then compare your answers with the provided solutions. Helpful resources:

  • This Review
  • Previous Exam (posted on the course webpage)
  • Homework; In particular, PAPER HOMEWORK!
  • Lecture Notes
  • Textbook
  • Online learning materials.

Some basic concepts/methods/theorems

  • Antiderivatives; Indefinite integral
  • Initial value problem;
  • Partition of an interval and the norm of a partition;
  • Riemann Sums. In particular, upper sum and lower sum
  • Sigma notation
  • Average of an integrable function
  • definite integral
  • The substitution rule for both indefinite integral and definite integral
  • Fundamental theorem of Calculus
  • Area between two curves
  • Calculate

∫ (^) f (x) g(x) h(t)dt.

  1. Find antiderivatives of f (x); i.e. find

f (x)dx. Example 1. (^) ∫ 2 x^2 + 3x^3 /^8 √ x dx

  1. Evaluate indefinite integrals using the substitution rule.

Example 2. (^) ∫ [xe^3 x 2

  • x sin(3x^2 )]dx

Example 3. (^) ∫ 1 √ x(1 +

x)^100

dx

  1. Evaluate definite integrals using the substitution rule

Example 4. (^) ∫ 16

2

dx 3 x

ln x

  1. Calculate d dx

∫ (^) f (x)

g(x)

h(t)dt.

Example 12. Find d dx

∫ (^) sin x

x^2

t^2 + 1dt

Example 13. Find d dx

∫ (^4) x 2

x^2

ln

tdt.