Please use Python to solve it

(50 points) Consider the definite integral I(cos(x2)) = foV 2 cos x?dx We cannot calcu- late its exact value but we can compute accurate approximations to it using Th (cos x). TA (cos x?) Th(cos x2) q(h) T. (cos x2) T. (cos x2) Let Using your code, find a value of h for which q(h) is approximately equal to 4. Get an approximation of the error, I(cos xa) Th (cos x2), for that particular value of h. Use this error approximation to obtain the extrapolated, improved, approximation 4 Sh(cos x2) = Tn (cos x?) +(T(cos x2) Th(cos 2?)) Explain why Sh(cos x2) is more accurate and converges faster to I(cos(x2)) than Th(cos x) Let S(cos x2) Sh(cos x2) 91(h) S (cosa?) - S, (cosa) Using your code, find a value of h for which q(h) is approximately equal to 16