They do a change of variables, x-a = u, so x= u+ag.lemaitre said:
The easiest way to see this is to notice that the integrand is an odd function (that is, f(-x) = -f(x)) and therefore the integral over an even interval [-n,n] is zero.g.lemaitre said:
Did they calculate the value for A before? What you are doing here is calculating an expectation value of a random variable, so it should be true thatg.lemaitre said:
Yes but you can't explain every single operation you do. It just seems to me you're trying to do assignments which are a bit too difficult for you. Maybe start from something easier?g.lemaitre said:
g.lemaitre said:
Integration using exponentials 2 is a method of finding the integral of a function that involves an exponential term in the form of e^x or a^x, where a is a constant. It is an advanced technique in calculus that is used to solve complex integrals.
The first step is to identify the function that needs to be integrated. Then, we use the power rule to integrate any terms without an exponent. Next, we use the substitution method to simplify the integral. Finally, we apply the integration by parts method to solve the integral.
Integration using exponentials 2 is used when the traditional methods of integration, such as substitution or integration by parts, are not suitable for solving the integral. It is also used to solve integrals that involve exponential functions, which are commonly found in physics and engineering problems.
One common mistake is forgetting to use the power rule to integrate terms without an exponent. Another mistake is not choosing the correct substitution to simplify the integral. It is also important to be careful with signs and constants when applying the integration by parts method.
No, integration using exponentials 2 is not suitable for all types of integrals. It is mainly used for integrals that involve exponential functions or integrals that cannot be solved using traditional methods. For other types of integrals, different techniques may be more effective.