Calculate M₁₀ and S₁₀ for the integral ∫¹₀ √1 − x² dx, whose value we know to be π/4 (one-quarter of the area of the unit circle).

(a) We usually expect S_N to be more accurate than M_N. Which of M₁₀ and S₁₀ is more accurate in this case?
(b) How do you explain the result of part (a)? The Error Bounds are not valid because |ƒ"(x)| and |ƒ⁽⁴⁾(x)| tend to ∞ as x → 1, but |ƒ⁽⁴⁾(x)| goes to infinity more quickly.