Using Simpson’s Rule Approximate the following integrals using Simpson’s Rule Experiment with values of n to ensure that the error is less than 10?3.

Problem 45EUsing Simpson’s Rule Approximate the following integrals using Simpson’s Rule Experiment with values of n to ensure that the error is less than 103. Answer; Step-1 of 2 ; In this problem we need to approximate the integral using simpson’s Rule experiment with values of n to ensure that the error is less than . Given integral is : dx The exact value of the given integral is : . simpson’s formula: Let us consider , f(x) = and n = 10 , = 0 , = , = ………...= f(0) = = = 4 , since cos(0) = 1 f( ) = =3.1814 f( ) = = -0.1982 f( ) = = 1.8346 f( 7) = = -0.3198 f( ) = = 0.8876 f( ) = = -0.3929 f( ) = =0.3284 f(9 ) = = -0.4321 f(5 ) = = 0 f( ) = = -0.44444Step-2 of 2; Therefore , [ 4 - 0.4444+ 4( 3.1814+0.8876+0 -0.3198 -0.4321) +2(1.8346+0.3284-0.1982-0.4444)] [ 3.5556 +4(3.3171) +2(1.5204)] 0.1048( 3.5556 +13.2684 +3.0408] 0.104 8( 19.872) 2.09439Weknow that , Absolute value = |exact value - approximate value| = |2.0943951 - 2.09439| = (5.1)