How to calculate (lim(0:1) ∫u dy)

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  • Thread starter Mickytenu
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In summary, to find the limit of a definite integral, you first evaluate the integral using the given bounds and then take the limit as the bound approaches the given limit. L'Hopital's rule can be used if the integral contains an indeterminate form. Calculating the limit is significant in finding exact areas and values, understanding function behavior, and using specific techniques such as substitution and integration by parts. The limit can be infinite if the function has a vertical asymptote within the bounds.
  • #1
Mickytenu
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Facing problem in solving 3 sets of ODE of second order.

1.∂2ψ/∂y2= 5 sinh(2ψ);

2.∂2u/∂y2= 20- ∂2ψ/∂y2;

3. ∂2T/∂y2= u*5/(lim(0:1) ∫u dy) + 15;


how to calculate (lim(0:1) ∫u dy) , while writing the MATLAB ode set of equations.
 
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  • #2
Some please write the MATLAB code and post..this will be a great help/
 

FAQ: How to calculate (lim(0:1) ∫u dy)

1. How do I find the limit of a definite integral?

To find the limit of a definite integral, you first need to evaluate the integral using the given bounds. Then, take the limit of this value as the bound approaches the given limit. For example, if the integral is ∫u dy from 0 to 1, you would first evaluate the integral as ∫u dy = [yu] from 0 to 1 = u. Then, take the limit of u as y approaches 1 to get the final limit value.

2. Can I use L'Hopital's rule to find the limit of a definite integral?

Yes, you can use L'Hopital's rule to find the limit of a definite integral. However, this is only applicable if the integral contains an indeterminate form, such as 0/0 or ∞/∞. In these cases, you can take the derivative of the numerator and denominator separately and then evaluate the limit again.

3. What is the significance of calculating a limit of a definite integral?

Calculating the limit of a definite integral can help in finding the exact area under a curve or the exact value of a quantity. It is also useful in finding the behavior of a function at a specific point and can provide valuable insights into the nature of the function.

4. Are there any specific techniques for calculating the limit of a definite integral?

Yes, there are specific techniques that can be used to calculate the limit of a definite integral, such as substitution, integration by parts, and trigonometric substitution. These techniques can make the evaluation process easier and quicker, especially for more complex integrals.

5. Can the limit of a definite integral be infinite?

Yes, the limit of a definite integral can be infinite. This can occur when the function being integrated has a vertical asymptote within the given bounds. In this case, the integral will not converge to a finite value, but rather approach infinity as the limit is evaluated.

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