Setting up Newton Raphson integral with matlab

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SUMMARY

The discussion focuses on using the Newton-Raphson method to numerically find the root of an equation involving an integral evaluated using the trapezoidal rule in MATLAB. The equation presented is 1 = e^{-cy} ∫_0^1 e^{-y(1-x)} dx. Participants clarify that the integral can be solved exactly rather than approximated, allowing for the application of Newton's Method to the resulting equation. The conversation highlights the importance of correctly identifying variables within the integral for successful implementation.

PREREQUISITES
  • Understanding of Newton-Raphson method for root finding
  • Familiarity with integral calculus, specifically the trapezoidal rule
  • Proficiency in MATLAB, particularly with symbolic computation using "syms"
  • Knowledge of exponential functions and their properties
NEXT STEPS
  • Research how to implement the trapezoidal rule in MATLAB for numerical integration
  • Learn about symbolic computation in MATLAB using the "syms" function
  • Study the application of Newton-Raphson method in solving nonlinear equations
  • Explore exact solutions for integrals involving exponential functions
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Mathematics students, engineers, and researchers involved in numerical analysis, particularly those working with MATLAB for solving equations involving integrals.

Moly
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Hi All.

I have an equation that i want to numerically find the root of by using Newton Raphson. However the equation involves an integral which i am using the trapazoidal rule to evaluate. And here is the simplified version of it:
1 = e^{-cy} \int_0^1 e^{-y(1-x)} dx

So i am supposed to integrate for x and then solve the resulting equation for values of y. How do i do that??

If i just wanted to do the integration, i would have used "syms" and found the result in terms of y... but i am totally stumped with this... please... SOS!
 
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Well, look inside the integral. The variable is x, y is a constant inside the integral. We can easily solve that integral exactly, no need to approximate that integral.

After that, you will have on the RHS some exponential terms divided by y, which is easy to apply Newtons Method to.
 
Thanks Gib.
I figured where i went wrong.. i still have a question that i will post later today
 

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