Evaluate the integral 1 integral13 dxx2 100 x232 Using the

Evaluate the integral 1 = integral_1^3 dx/x^2 (100 - x^2)^3/2 Using the Romberg Integration up to 32 segments. Using Gauss-Legendre quadrature with different number of gauss points (2,3,4). Given that the exact vale of the integral is 1 = 1/100 [- squareroot 100 - x^2/x + x/squareroot 100 - x^2]_1^3 Compare the approximated results by finding the error in each case

Solution

Method Estimate of the integral by the method Romberg with 32 6.9841 G-L (n=2) 6.76367 G-L (n=3) 6.960990 G-L (n=4) 6.981885 Exact Evaluation 6.9840