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Integrals - Calculus for the Biological Sciences - Exam, Exams of Calculus

Amity University - BiharCalculus

This is the Exam of Calculus for the Biological Sciences which includes Value Problem, Initial, Substitution, Antiderivatives, Rewriting The Integrand, Propelled, Least One Number, Boxes etc. Key important points are: Integrals, Statement, Evaluate, Continuous, Differentiable, Integrable, Region, Graph, General Antiderivative, Compute

Typology: Exams

2012/2013

Uploaded on 02/18/2013

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Simon Fraser University
MATH 155 - MIDTERM 1 (Version A)
Instructor:N.Kouzniak
June 1, 2005
Last Name
Given Name(s)
Student 10
Signature
INSTRUCTIONS
1. Do not open this booklet until
instructed to do so. The bookletcontains
6 pages includingthe coverpage.
2. Print your name and student 10 inthe
space provided above.
3. For each question you must show all
your work unlessstatedotherwise.
4. No book, paper, or device other than the
usual writing instruments, this booklet, and
scientific calculators are allowed. In
particular, no graphing/programmable
calculators are allowed.
5. During this examination, speaking to,
communicating with, or exposing written
papers to the view of other students is
forbidden.
6. You may use the back of the previous
page for a roughwork or if you runout of
space.
7. Stop writing when you are instructed to
do so. Failure to follow instructions may
result in penalties.
1
Question Maximum Mark
110
2 2
32
42
5 11
6 10
73
Total 40
pf3
pf4
pf5

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Simon Fraser University

MATH 155 - MIDTERM 1 (Version A)

Instructor: N.Kouzniak

June 1, 2005

Last Name

Given Name(s)

Student 10

Signature

INSTRUCTIONS
  1. Do not open this booklet until instructed to do so. The booklet contains 6 pages includingthe coverpage.
  2. Print your name and student 10in the space provided above.
  3. For each question you must show all

your work unlessstatedotherwise.

  1. No book, paper, or device other than the usual writing instruments, this booklet, and scientific calculators are allowed. In particular, no graphing/programmable calculators are allowed.
  2. During this examination, speaking to, communicating with, or exposing written papers to the view of other students is forbidden.
  3. You may use the back of the previous page for a rough work or if you run out of space.
    1. Stop writing when you are instructed to do so. Failure to follow instructions may result in penalties.

Question Maximum^ Mark

(^1 )

2 2

3 2

(^4 )

5 11

6 10

7 3

Total (^40)

  1. [10 marks] Indicate whether the statement is True or False. Do not evaluate the integrals

Statement

(^1) JCSC2 xdx = -cot x + C

2 Ik = n(n+1)

k=1 6

If f(x) is continuous on [a,b], then the function defined by x F(x) = Jf(u)du, a ~ x ~ b 3 a is continuous on [a,b] and differentiable on (a,b) with d -F(x) = f(x) dx

1 J

dx 1 J

dx o(1+X+X3)1/2 ~ o(1+2x+X3)1/

b n J~1+X2dx = L~1+ct~Xk a k=

6

If 0 ~ Jsinxdx ~ 7r 0

7

1 dx J~=-^2 -1 X

8

If/2 If If/ J cosxdx = JCOSxdx + J cosxdx 0 0 If

If f(x) is integrable on[a,b], then b Jf(x)dx =[area of the region between the graph of f(x) and x-axis] a

10 I The most general antiderivative of a function f(x) is F(x)+C, where F(x) = f'(x)

T F
  1. [11 marks total] Express the following quantities in terms of the definite integrals. DO NOT EVALUATE the integrals.

i) The volume of the solid obtained by rotating the region bounded by the curves y = 'Vi, x = 4 Y in the first quadrant:

  1. [3 marks] aboutthe x-axis
    1. [3 marks] about the y-axis

ii) [3 marks] The area A of the region enclosed between the curves y = X2, Y = (x - 2)2 and the line y = 0.

iiO [2 marks] The average value of y = cotx over [7Z"/4,7Z"/3]
  1. [10 marks total] Evaluate the following integrals

a) [2 marks] fsinxcos2 xdx

2

b) [4 marks] fx.JX=1dx

1