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Question No: 1                                                                           Marks =10

 

Evaluate the line integral

 

 

Question No: 2                                                                           Marks =10

 

Use Green’s Theorem to evaluate I =  around the boundary c, the ellipse x2 + 4y2 = 25.

 

 

 

Question No: 3                                                                             Marks = 5

 

    Find curl of vector F where F =

 

                                                           

 

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Replies to This Discussion

Please Discuss here about this assignment.Thanks
upload solved question of assingment # 4

yar ap mje ye byao k 1st question ka method kiya hoga matlab x2+4y2=25   ye kiya hy agher simple integrate kerna hy to wo to ho jaye ga.

or 2nd question ka theorm wala question half hota hy half nahi

Q1

To answer this question, split up the line integral into two pieces:

intc (x + 2y)dx   and   intc (x - y)dy.

Our parameter is t,  0<=t<=pi/4    (I assume, because your problem statement gives inf <-- t < 0, which diverges )

We need to convert dx, dy  into dt:

x = 2 cos t   -->  dx = -2 sin t dt

y = 4 sin t  -->  dy = 4 cos t

Now,

intc (x + 2y)dx = int [ (2 cos t + 8 sin t) ( -2 sin t ) dt , 0<= t <=pi/4]

= int [ -4 costsint - 16sint^2, 0<= t <=pi/4 ]

And,

= intc (x - y)dy = int [ (2 cos t - 4 sin t) ( 4 cos t ) dt , 0<= t <=pi/4]

= int [ 8 cost^2 - 16 costsint, 0<= t <=pi/4 ]

So,

intc (x + 2y)dx  + intc (x - y)dy = int[ 8 cost^2 - 20 costsint - 16 sint^2, 0<= t <=pi/4 ]

=-4 t + 5 cos(2 t) + 6 sin(2 t) + C, evaluated from 0<=t<=pi/4

= 1 - pi = 2.14

 

Q2 Answer

Note that the ellipse has standard form x²/2² + y²/(5/2)² = 1.
Denoting R as the region inside C, we have

∫c [(3x - 2y) dx + (3y + 2x) dx]
= ∫∫R [(∂/∂x)(3y + 2x) - (∂/∂y)(3x - 2y)] dA, by Green's Theorem
= ∫∫R (2 - (-2)) dA
= 4 ∫∫R dA
= 4 * (Area of the ellipse)
= 4 * (π * 2 * (5/2))
= 20π.

Please upload mth301 assignment#4 solution file.
yar plz question 3 ka idea solution doo
yar plz ap mujy pehly 2 question de doo
Download Atatchment..!!
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