Design and construct a computer program in C++ languages Your program will use three different 5-point numerical quadrature methods (Closed Newton Cotes, Gaussian Quadrature, and Lobatto Quadrature)

You will employ each of these methods to solve each of the following three problems to find the area under the respective curves over the interval (-1, 1)

the first function f(x) = 1 - sin(1 - x) (The true area under the above curve is (to 20 digits) 0.58385316345285761300)

the second function f(x) = sqrt(x + 1) + 1 (The true area under the above curve is (to 20 digits) 3.8856180831641267317)

the third function f(x) = tanh(x+1) (The true area under the above curve is (to 20 digits) 1.3250027473578644309)

First, print out the values of the weights and the nodes for each quadrature formula, Then for each function (or curve), print out your approximation to the area under the curve, the true value of the area, and the error in the approximation for each of the three quadrature formulae. Write down any conclusions that you can make from these experiments.

Note: For Lobatto quadrature, the nodes are x[1] = -1, x[2] = -sqrt(3/7), x[3] = 0, x[4] = sqrt(3/7), and x[5] = 1. The weights are w[1] = 1/10, w[2] = 49/90, w[3] = 32/45, w[4] = 49/90, and w[5] = 1/10.