exercise explore rounding errors with large numbers the trapezoidal method integrates linear functions exactlyand this property was used in the test function test_trapezoidal_linear in the file test_ trapezoidal py change the function used in sect to xd and rerun the test what happenshow must you change the test to make it usefulhow does the convergence rate test behaveany need for adjustmentfilenametest_trapezoidal py exercise write test functions for xdx we want to test how the trapezoidal function works for the integral xdx two of the tests in test_trapezoidal py are meaningful for this integral compute by hand the result of using or trapezoids and modify the test_ trapezoidal_one_exact_result function accordingly then modify test_ trapezoidal_conv_rate to handle the square root integral filenametest_trapezoidal py remarks the convergence rate test fails printing out shows that the actual convergence rate for this integral is : and not the reason is that the error in the trapezoidal is / for some (unknown oeabwith method xd xf  as pointing to potential problem in the size of the error running test with say : xdx shows that the convergence rate is indeed restored to exercise rectangle methods the midpoint method divides the interval of integration into equal-sized subintervals and approximates the integral in each subinterval by rectangle whose height equals the function value at the midpoint of the subinterval insteadone might use either the left or right end of the subinterval as illustrated in fig this defines rectangle method of integration the height of the rectangle can be based on the left or right end or the midpoint fig illustration of the rectangle method with evaluating the rectangle height by either the left or right point