# Type 6 Laplace Transform of Integrals Problem 2 - Laplace Transform - Engineering Mathematics 3 | Summary and Q&A

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April 2, 2022
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Ekeeda
Type 6 Laplace Transform of Integrals Problem 2 - Laplace Transform - Engineering Mathematics 3

## TL;DR

This video discusses problem 2 on the Laplace transform of integrals and provides a step-by-step solution.

## Questions & Answers

### Q: What is the first step in solving problem 2 on Laplace transform of integrals?

The first step is to rewrite the given function in terms of u, ensuring that everything inside the integration is also in terms of u. Constants and variables not in terms of u should be taken out of the integration.

### Q: What are the different steps involved in solving the problem?

The steps include finding the Laplace of cos^2u, multiplying the result by u, applying Laplace transform to the integral, and finally applying the Final Value Theorem.

### Q: What is the difference in approach if the problem is taken as e^-u instead of cos^2u?

If the problem is interpreted as e^-u, the Laplace transform and multiplication steps will differ. The solution will also be different, so it is important to identify the correct variable in the problem.

### Q: How can the Laplace transform of integrals be applied to the given problem?

The Laplace transform of integrals is applied by multiplying the terms with a factor of 1/s^2 and integrating it over the appropriate range. This step helps in solving the problem systematically.

## Summary & Key Takeaways

• The problem involves breaking down the given function, cos^2u, into terms of u, and then applying Laplace transform techniques.

• The order of execution is: finding the Laplace of cos^2u, multiplying by u, applying Laplace transform to the integral, and finally applying the Final Value Theorem.

• The video highlights the importance of correctly identifying the terms and constants in order to solve the problem accurately.

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