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MTH301 Spring 2012 Assignment: Integration and Green's Theorem, Exercises of Mathematics

Institute of Mathematical SciencesMathematics

An assignment for the mth301 course in the spring 2012 semester. The assignment includes six questions related to integration and green's theorem. Students are required to evaluate double integrals, line integrals, and find limits of integration and arc lengths. Use of ms word and individual submission is mandatory.

Typology: Exercises

2011/2012

Uploaded on 08/03/2012

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Assignment # 3
MTH301 (Spring 2012)
Total marks: 10
Lecture # 22 to 37
DON’T MISS THESE Important instructions:
Only Question # 3 is graded. Remaining questions are for your practice only
therefore, you do not need to send the solution of non-graded questions.
All students are directed to use the font and style of text as is used in this
document.
This is an individual assignment, not group assignment, so keep in mind that you
are supposed to submit your own, self made & different assignment even if you
discuss the questions with your class fellows. All similar assignments (even with
some meaningless modifications) will be awarded zero marks and no excuse will
be accepted. This is your responsibility to keep your assignment safe from
others.
Solve the assignment on MS word document and upload your word (.doc) files only
Question # 1
Evaluate the following double integral
cos 3
00
rdrd


Question # 2
Evaluate the following line integral with respect to arc-length s
2
1
C
xds
y



where C is the line 1 2 , 0 1
x
t y t and t 
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Download MTH301 Spring 2012 Assignment: Integration and Green's Theorem and more Exercises Mathematics in PDF only on Docsity!

Assignment # 3

MTH301 (Spring 2012)

Total marks: 10 Lecture # 22 to 37

DON’T MISS THESE Important instructions:

Only Question # 3 is graded. Remaining questions are for your practice only therefore, you do not need to send the solution of non-graded questions.  All students are directed to use the font and style of text as is used in this document.  This is an individual assignment, not group assignment, so keep in mind that you are supposed to submit your own, self made & different assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others.  Solve the assignment on MS word document and upload your word (.doc) files only

Question # 1

Evaluate the following double integral

cos 3

0 0

r dr d

 

Question # 2

Evaluate the following line integral with respect to arc-length s

C

x ds y

where C is the line x  1  2 , t yt and 0  t  1

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Question # 3

    2 2 3

Use Green’s Theorem to evaluate 2

where C is a square with vertices at (0, 0), (2, 0), (2, 2), (0, 2)

C

x^ ^ xy^ dx^ ^ y^  x y^ dy

Question # 4

Find the limit of integration for integrating f ( , r    over the region R that lies inside the

cardioid r  cos  and outside the circle r  3.

Question # 5

Find the arc length of parametric curve

x (1  t ) 2   y (1  t )^3  where  0  t  1

Question # 6

Evaluate the line integral

2 c I  (^)  x ydx  xdy

where c comprises the three sides of the triangle joining O(0, 0), A (2, 0) and B (1, 1).

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