Finding the Laplace Transform of f(t) = (t + 2)^3 | Summary and Q&A

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October 19, 2014
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The Math Sorcerer
Finding the Laplace Transform of f(t) = (t + 2)^3

TL;DR

The video explains how to find the Llaplace transform of the equation T + 2 Quan cubed solution.

Key Insights

• 😑 Pascal's triangle is a useful tool for finding coefficients in mathematical expressions.
• ⌛ The Llaplace transform is a mathematical operation used to convert a function of time into a function of complex frequency.
• ❓ The Llaplace transform of a constant function is given by 1/s.
• ✊ The Llaplace transform of a power function is obtained by multiplying the function by s raised to the power of the exponent and integrating it.

Transcript

all right we have to find the llao transform of t + 2 Quan cubed solution so um we have to multiply this out so I'm going to draw Pascal's triangle over here so one and then you write ones in the side and then 1 plus one is two so one one and then you add so you get three three one's on the side I stopped here because this is row zero this is Row o... Read More

Q: How do you find the coefficient for each term when applying Pascal's triangle?

To find the coefficient for each term, you use the rows of Pascal's triangle. The number in each row corresponds to the power of the term, and the number of times it appears in the expression.

Q: Can you simplify the expression for the Llaplace transform further?

The expression for the Llaplace transform can be simplified by combining like terms. In this case, you can combine the terms with the same power of s to get a more concise representation.

Q: Why is the Llaplace transform of 1 equal to 1/s?

The Llaplace transform of 1 is equal to 1/s because the Llaplace transform of a constant function is given by 1/s.

Q: Is it necessary to show all the steps when finding the Llaplace transform?

It is not necessary to show all the steps when finding the Llaplace transform. You can skip some steps to make the process more efficient, as long as you understand the underlying concepts and calculations.

Summary & Key Takeaways

• The Llaplace transform of T + 2 Quan cubed solution is derived by multiplying it out and applying Pascal's triangle.

• The coefficients for each term in the expression are obtained by using the rows of Pascal's triangle.

• The resulting Llaplace transform is equal to 6/(s^4 + 6) + 12/s^3 + 12/s^2 + 8/s.