Perform the integral numerically

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In summary, the conversation is about finding the speed and time of fall for an object released from rest at an altitude above Earth's surface. The speed at a distance r is given by v = sqrt(2GME (1/r -1/ (RE + h)), and the time of fall can be calculated using the integral (Delta) t = - (integral from i to f) dr/v, with a negative sign due to the object moving opposite to the radial direction. The conversation also mentions that the question belongs in the Homework & Coursework subforum and that the poster needs to show their attempt at a solution for others to help.
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prabhjyot
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need help please urgent

An object is released from rest at an altitude h above the surface of the Earth. (a) Show that its speed at a distance r from the Earth’s center, where RE < r < RE + h, is given by
v = sqrt(2GME (1/r -1/ (RE + h) )

(b) Assume the release altitude is 500 km. perform the integral:
(Delta) t = (integral from i to f) dt = - (integral from i to f) dr/v

to find the time of fall as the object moves from the release point to the Earth’s surface. The negative sign appears because the object is moving opposite to the radial direction, so its speed is v = -dr / dt. Perform the integral numerically.
 
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1. This belongs in the Homework & Coursework subforum.
2. We can not help you unless you follow the posting guidelines and first show your attempt at a solution.
 

1. What does it mean to "perform the integral numerically"?

Performing the integral numerically refers to the process of using numerical methods to approximate the value of a definite integral, rather than finding an exact solution using analytical techniques.

2. What are some common numerical methods used to perform integrals?

Some common numerical methods for integration include the trapezoidal rule, Simpson's rule, and Gaussian quadrature. These methods use a combination of function evaluations and interpolation to approximate the value of the integral.

3. How accurate are numerical methods for integration?

The accuracy of numerical methods for integration depends on the specific method used and the complexity of the function being integrated. In general, these methods can provide accurate results up to a certain number of decimal places, but they may introduce some error due to the approximation process.

4. Can numerical methods be used for any type of integral?

Numerical methods can be used for most types of integrals, including definite and indefinite integrals, single and multiple integrals, and integrals with both real and complex-valued functions. However, the complexity of the integral may affect the accuracy and efficiency of the method chosen.

5. How do you know which numerical method to use for a specific integral?

The choice of numerical method depends on the function being integrated, the desired accuracy, and the resources available. It is important to consider the strengths and limitations of each method and choose the one that is most suitable for the given problem.

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