Computing integration with the Trapezoidal Rule
I am trying to implement the trapezoidal rule programmatically but am having trouble finding a good way to input the function of x and then have a loop which will iterate through for each sub-interval finding the area of the trapezium and adding the results and returning it.
How to prove a specific integral formula
How to prove the following formula? Integrate[x^(2n)/sqrt(1-x^2),{x,-1,1}] =Pi*(2n)!/(4^n*n!^2)