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KOC University - Calculus I Exam (MATH 106) - Final Exam (January 9, 2012), Exams of Calculus

Tamil Nadu Open UniversityCalculus

The instructions and problems for the final exam of calculus i (math 106) at koc university. The exam covers topics such as integration, improper integrals, critical points, and derivatives. Students are not allowed to use calculators, books, or notes during the exam and must explain their answers. The exam consists of 10 problems and lasts for 135 minutes.

Typology: Exams

2012/2013

Uploaded on 03/21/2013

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KOC¸ UNIVERSITY
MATH 106 - CALCULUS I
Final Exam January 9, 2012
Duration of Exam: 135 minutes
INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.
No books, no notes, no questions and no talking allowed. You must always explain your
answers and show your work to receive full credit. Use the back of these pages if nec-
essary. Print (use CAPITAL LETTERS) and sign your name, and indicate your
section below.
Surname, Name: —————————————————
Signature: ————————————————————
Section (Check One):
Section 1: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 12:30) —–
Section 2: E. S¸. Yazıcı(Mon-Wed-Fri 14:30) —–
Section 3: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 10:30) —–
Section 4: E. S¸. Yazıcı(Mon-Wed-Fri 11:30) —–
Section 5: T. Etg¨u (Tue-Thu 12:30) —–
PROBLEM POINTS SCORE
1 18
2 7
3 10
4 10
5 10
6 10
7 12
8 10
9 10
10 12
TOTAL 109
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KOC¸ UNIVERSITY

MATH 106 - CALCULUS I

Final Exam January 9, 2012

Duration of Exam: 135 minutes

INSTRUCTIONS: CALCULATORS ARE NOT ALLOWED FOR THIS EXAM.

No books, no notes, no questions and no talking allowed. You must always explain your

answers and show your work to receive full credit. Use the back of these pages if nec-

essary. Print (use CAPITAL LETTERS) and sign your name, and indicate your

section below.

Surname, Name: —————————————————

Signature: ————————————————————

Section (Check One):

Section 1: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 12:30) —– Section 2: E. S¸. Yazıcı(Mon-Wed-Fri 14:30) —– Section 3: S. K¨u¸c¨uk¸cif¸ci (Mon-Wed-Fri 10:30) —– Section 4: E. S¸. Yazıcı(Mon-Wed-Fri 11:30) —– Section 5: T. Etg¨u (Tue-Thu 12:30) —–

PROBLEM POINTS SCORE

1 18 2 7 3 10 4 10 5 10 6 10 7 12 8 10 9 10 10 12 TOTAL 109

  1. Evaluate the following integrals.

a) (5 pts.)

x(1 + ln x)

dx

b) (6 pts.)

x arctan x dx

  1. Determine whether the following improper integrals are convergent or divergent.

a) (5 pts.)

0

dx

x − 1

dx

b) (5 pts.)

1

| sin x|

x^2

dx

4.(10 pts.) Find

1

(x

2

  • x) dx using the definition of the definite integral.

7.(12 pts.) Find the area of the region bounded by y = x 3 − 1 and y = 3x 2 − 3 x between

x = 0 and x = 2.

8.(10 pts.) Let R be the region enclosed by y = x 3 and y = x 2

. Calculate the volume of

the solid obtained by rotating R about y = − 1.

9.(10 pts.) Find the coordinates of the point P on the curve y =

x such that the

x-intercept of the tangent line to this curve at P is − 1.