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 :
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (a)
Explanation: Let y(x) = c
Question 2: Solve:
(a)
(b)
(c)
(d) None of the above
Answer: (a)
Explanation:
Question 3: Solve :
(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:
Question 4: Find lambda :
if y(x)=x
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (c)
Explanation:
Question 5: Solve:
(a)
(b)
(c)
(d)
Answer: (a)
Explanation: In this problem f(x)=x and k(x-y)=x-y
Take the laplace transform on both sides.
Question 6: For the integral equation:
then y(-3) is
(a) -2,1
(b) -3,1
(c) 1,1
(d) 1,-1
Answer: (c)
Explanation:
Question 7: Find the eigenvalue lambda :
(a) 1/2
(b) 1/4
(c) 1/3
(d) 1/6
Answer: (b)
Explanation:
Question 8: Solve:
Answer: (a)
Explanation:
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.
Question 10: Solve:
Answer: (a)
Explanation:
