Question: Let (x) = sin(x 2 ) and I = 1 0 (x) dx. (a) Check that f'(x) = 2 cos(x) - 4x sin(x). Then

Let ƒ(x) = sin(x²) and I = ∫¹₀ƒ(x) dx.

(a) Check that f'(x) = 2 cos(x) - 4x sin(x). Then show that f

(a) Check that f'(x) = 2 cos(x) - 4x sin(x). Then show that f"(x)| 6 for x = [0, 1]. 12 cos(x)| 2 and 14x sin(x)| 4 for x [0, 1]. 1 (b) Show that Error(MN) is at most 4N (c) Find an N such that I - MN| 10-.

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