In Python

(50 points) Consider the definite integral I (cos(x2) = SV 3 cos x?dx We cannot calculate its exact value but we can compute accurate approximations to it using Th(cos x). Let Ty (cos x?) T, (cos 22) q(h) Th(cosc) T (cos z) 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 x2) Th (cos x2), for that particular value of h. Use this error approximation to obtain the extrapolated, improved, approximation Sr (cos x) = T, cos x2 + 3 (Ty (cos x) Ty(cos x?)) Explain why Sh(cos x2) is more accurate and converges faster to I(cos(x2) than Thcos x2 Let Sy (cos x2) Sh(cos x2) 91(h) S4 (cos 22) Sy (cos x2) Using your code, find a value of h for which q 1(h) is approximately equal to 16. 2 (50 points) Consider the definite integral I (cos(x2) = SV 3 cos x?dx We cannot calculate its exact value but we can compute accurate approximations to it using Th(cos x). Let Ty (cos x?) T, (cos 22) q(h) Th(cosc) T (cos z) 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 x2) Th (cos x2), for that particular value of h. Use this error approximation to obtain the extrapolated, improved, approximation Sr (cos x) = T, cos x2 + 3 (Ty (cos x) Ty(cos x?)) Explain why Sh(cos x2) is more accurate and converges faster to I(cos(x2) than Thcos x2 Let Sy (cos x2) Sh(cos x2) 91(h) S4 (cos 22) Sy (cos x2) Using your code, find a value of h for which q 1(h) is approximately equal to 16. 2