Show formally that (a) * Jo(x)dx = 1; 0 (b) Jo(x)= = Π 11f" cos (x cost) dt. " πο For Section 51 number 6b, expand cos(x cost) as ∞ Σ(-1)" x2n cos2n t (2n)! n=0 and integrate this from t = 0 tot = π by integrating each term individually (you don't have to justify why this works, which is why the question says "formally"). You will need the fact that 1 πT H=/ SP Cos²n t dt = 2n (27) (2n)! 22n (n!)² This gives you a power series in x; compare the coefficients to those derived in the text for Jo (x). They will be the same, so the two functions are equal.