def gauss(f, N, a = -1, b = 1):
    [x,w] = leggauss(N)
    x = (b-a)*(x+(a+b)/(b-a))/2
    w = (b-a)*w/2
    return np.dot(w,f(x))
def f(x):
    return np.sin((np.pi/2)*(x**2))


a=0
b=.75
err=10**-5+1
N=100
itr=0
while(np.fabs(err)>10**-5):
    err=(gauss(f,N,a,b)-.5)/f(b)
    b=b-(gauss(f,N,a,b)-.5)/f(b)
    itr+=1
print(b)
print(itr)
print(f'true error = {np.fabs(fresnel(b)[0]-0.5)}')