Practice Proof of the Theorem - 6.3 | 6. Laplace Transform of an Integral | Mathematics - iii (Differential Calculus) - Vol 1
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the definition of the Laplace Transform?

πŸ’‘ Hint: What does it do to a time domain function?

Question 2

Easy

What theorem allows the interchange of integration order?

πŸ’‘ Hint: Recall its significance in multivariable calculus.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What is the formula for the Laplace Transform of an integral?

  • L{∫f(Ο„)dΟ„} = F(s)
  • L{∫f(Ο„)dΟ„} = F(s)/s
  • L{∫f(Ο„)dΟ„} = s*F(s)

πŸ’‘ Hint: Recall how integration affects the transformation.

Question 2

True or False: The Laplace Transform can only be applied to continuous functions.

  • True
  • False

πŸ’‘ Hint: Think about the types of functions we defined earlier.

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Challenge Problems

Push your limits with challenges.

Question 1

Prove the theorem that L{f(t)} = F(s) implies L{∫f(Ο„)dΟ„} = F(s)/s by evaluating in detail each step including usage of Fubini's theorem.

πŸ’‘ Hint: Carefully track changes in limits during integration and remind yourself of the definition throughout.

Question 2

How would you apply the theorem to analyze a capacitor charging described by a differential equation?

πŸ’‘ Hint: Remember to define your variables clearly before applying any transforms.

Challenge and get performance evaluation