Evaluate (t-tau)*sin(a*tau) with respect to tau, tau = 0t

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In summary, evaluating the function (t-tau)*sin(a*tau) with respect to tau allows us to find the value of the function at a specific point, in this case when tau is equal to 0t. This can provide insight into the behavior and properties of the function at that point. "Evaluate" in this context means substituting the given value of tau into the function and solving for the resulting expression. This function can be evaluated at any value of tau, but evaluating it at tau = 0t can help us understand its behavior and identify any special properties at that point. Evaluating at other values of tau can provide a better understanding of the overall behavior and properties of the function.
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lkj-17
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Both Int {(t-tau)*sin(a*tau)}d(tau) and Int {(tau)*sin(a*(t-tau)}d(tau) will give the same answer (a*t-sin(a*t))/(a^2), where tau = 0..t

Anybody can give a hint how to do the integration.

Personally, I think neither integration by parts nor substitution are suitable methods.
 
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  • #2
The first integral can be easily done with integration by parts. For the second integral, use the sum-of-angles formula and then integrate by parts.
 

FAQ: Evaluate (t-tau)*sin(a*tau) with respect to tau, tau = 0t

1. What is the purpose of evaluating (t-tau)*sin(a*tau) with respect to tau?

The purpose of evaluating this function with respect to tau is to find the value of the function at a specific point, in this case when tau is equal to 0t. This can provide insight into the behavior and properties of the function at that point.

2. What does the term "evaluate" mean in this context?

In this context, "evaluate" refers to substituting the value of tau (in this case, 0t) into the given function and solving for the resulting expression. This will give the numerical value of the function at that particular point.

3. How do you evaluate (t-tau)*sin(a*tau) with respect to tau?

To evaluate this function with respect to tau, you would first substitute 0t in place of tau, giving (t-0t)*sin(a*0t). This simplifies to t*0*sin(0), which equals 0. Therefore, the value of the function at tau = 0t is 0.

4. What is the significance of evaluating (t-tau)*sin(a*tau) at tau = 0t?

Evaluating the function at tau = 0t allows us to understand how the function behaves at that specific point. It can also help us to identify any special properties or characteristics of the function at that point.

5. Can this function be evaluated at other values of tau?

Yes, this function can be evaluated at any value of tau. However, the resulting value will vary depending on the value of tau chosen. Evaluating the function at different values of tau can provide a better understanding of the overall behavior and properties of the function.

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