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Integral Equation:

Integral Equation is the equation with unknown function inside the one or more  integral signs. It carries a vast application in framing mathematical models for several real life engineering problems. It contributes in the field of quantum mechanics, waves and theoretical physics.

 

Integral Equation Sample Questions:

Question 1: Find lambda :


Question 1

 

(a) 0

(b) 1

(c) 2

(d) 3


Answer: (a)

Explanation: Let y(x) = c

 

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Question 2: Solve:



Question 2

 

(a) Question 2 a

(b) Question 2 b

(c) Question 2 c

(d) None of the above


Answer: (a)

Explanation:

Explanation 2

 

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Question 3: Solve :


Question 3

 

(a) Question 3 a

(b)  ∫ a^x dx = (ax/ln a) + C ; a>0,  a≠1

(c) (1/x) dx = ln |x| + C

(d) ∫ csc x ( cot x) dx = – csc x + C


Answer: (a)

Explanation:

Explanation 3

 

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Question 4: Find lambda :



>Question 4

 

 
if y(x)=x

 

(a) 1

(b) 2

(c) 3

(d) 4


Answer: (c)

Explanation:

Explanation 4

 

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Question 5: Solve:


Question 5

 

(a) Question 5 a

(b) Question 5 b

(c) Question 5 c

(d) Question 5 d


Answer: (a)

Explanation: In this problem f(x)=x and k(x-y)=x-y
Take the laplace transform on both sides.

 

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Question 6: For the integral equation: 


Question 6


Question 6.1


then y(-3) is

 

(a) -2,1

(b) -3,1

(c) 1,1

(d) 1,-1


Answer: (c)

Explanation:

Explanation 6

 

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Question 7: Find the eigenvalue lambda  :


Question 7

 

(a) 1/2

(b) 1/4

(c) 1/3

(d) 1/6


Answer: (b)

Explanation:

Explanation 7

 

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Question 8: Solve: 


Question 8

 

Question 8.1


Answer: (a)

Explanation: 

Explanation 8

 

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Question 9: An object falling from a bridge with velocity vt=-5t-4 ms. Find the height of the bridge, if the object touches the ground after t=10 seconds.

 

(a) 290 m

(b) 90 m

(c) 200 m

(d) 120 m


Answer: (a)

Explanation: To find the vertical position of the object, we need to integrate the velocity equation with respect to time.

 

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Question 10: Solve:
 

Question 10

 

Question 10.1

Answer: (a)

Explanation:

Explanation 10

 

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