Practice Related Properties and Extensions - 6.8 | 6. Laplace Transform of an Integral | Mathematics - iii (Differential Calculus) - Vol 1
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Related Properties and Extensions

6.8 - Related Properties and Extensions

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Practice Questions

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Question 1 Easy

What is the theorem related to the Laplace Transform of an integral?

💡 Hint: Think about how integration affects the Laplace Transform.

Question 2 Easy

What does the term 'convolution' mean?

💡 Hint: Consider how two signals might interact.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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

L{∫f(τ)dτ} = F(s) * s
L{∫f(τ)dτ} = F(s)/s
L{∫f(τ)dτ} = s * F(s)

💡 Hint: Think about how integrating affects the Laplace Transform.

Question 2

The Convolution Theorem states that L{f∗g} is equal to which of the following?

F(s) + G(s)
F(s) - G(s)
F(s) * G(s)

💡 Hint: Consider how responses from different functions combine.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a function f(t) = e^(-at), find L{∫f(τ)dτ} and discuss its implications in a physical system.

💡 Hint: Remember to apply the theorem correctly and consider the context of physical systems.

Challenge 2 Hard

For two functions f(t) = e^(2t) and g(t) = sin(at), find L{f∗g} and explain its significance in signal processing.

💡 Hint: Dissect the convolution theorem step by step.

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