Write a python program for the following problem

1 = (sin-/100x dx Evaluate the integral using the Romberg integration technique. Have your program print out a triangular table of values, as on page 161 (shown below), of all the Romberg estimates of the integral. Calculate the error on your estimates using Eq. (5.49) and again continue the calculation until you reach an accuracy of = 10-6. You should find that the Romberg method reaches the required accuracy considerably faster than the trapezoidal rule alone. Perhaps a picture will help make the process clearer. This diagram shows which values are needed to calculate further Rs. h = R1,1 12 = R21 R22 R1 - Rx - R33 1x = R1 R22 R23 R (5.47) (5.48) I= Rim + Cim?+ (1+2), I = R3-1, + Cm P**"+O(h*1+2) = R-1, +4"*C mh?+ (2m +2). Equating the two and rearranging we have Comh?" = 1 (Rim Ri-1m) +O(27w+2), and substituting this into Eq. (5.47) gives 1 = Rim+1+O(42m +2), (5.49) (5.50) where Rim+1 = Rim+ Rim - R:-), (5.51) 1 = (sin-/100x dx Evaluate the integral using the Romberg integration technique. Have your program print out a triangular table of values, as on page 161 (shown below), of all the Romberg estimates of the integral. Calculate the error on your estimates using Eq. (5.49) and again continue the calculation until you reach an accuracy of = 10-6. You should find that the Romberg method reaches the required accuracy considerably faster than the trapezoidal rule alone. Perhaps a picture will help make the process clearer. This diagram shows which values are needed to calculate further Rs. h = R1,1 12 = R21 R22 R1 - Rx - R33 1x = R1 R22 R23 R (5.47) (5.48) I= Rim + Cim?+ (1+2), I = R3-1, + Cm P**"+O(h*1+2) = R-1, +4"*C mh?+ (2m +2). Equating the two and rearranging we have Comh?" = 1 (Rim Ri-1m) +O(27w+2), and substituting this into Eq. (5.47) gives 1 = Rim+1+O(42m +2), (5.49) (5.50) where Rim+1 = Rim+ Rim - R:-), (5.51)