How to integrate -exp((s^2 - t^2)/2)*(f'(t) - t*f(t)) dt

  • Thread starter lamba89
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In summary, The conversation discusses using Wolfram Alpha to solve an integral for the PDE exam. The person is unsure how the solution was obtained and someone suggests using the product rule for differentiation. The person then realizes the solution themselves.
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  • #2
Apply the product rule for differentiation to the solution. This gives you the integrand. If you recognize this then you just need to do the reverse to get the solution.
 
  • #3
Thanks, I just realized it too
 

Related to How to integrate -exp((s^2 - t^2)/2)*(f'(t) - t*f(t)) dt

1. What is the meaning of integration?

Integration is a mathematical process that involves finding the area under a curve. It is often used to solve problems involving motion, change, and accumulation.

2. How do I integrate a function?

To integrate a function, you first need to find the antiderivative of the function, which is the function that when differentiated, gives you the original function. Then, you can use the fundamental theorem of calculus to evaluate the integral.

3. What is the purpose of -exp((s^2 - t^2)/2)*(f'(t) - t*f(t)) in the integration process?

This term is a specific type of integrand, meaning it is the function being integrated. It is used to represent a specific problem or scenario, and by integrating it, we can find the solution to that problem.

4. Can integration be used in real-world applications?

Yes, integration is used in various fields such as physics, engineering, economics, and more. It can be used to solve problems involving rates of change, optimization, and finding areas and volumes.

5. Are there different methods for integration?

Yes, there are various methods for integration, such as substitution, integration by parts, partial fractions, and more. The choice of method depends on the specific problem and the function being integrated.

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