Let (x) = sin(x 2 ) and I = 1 0 (x) dx. (a) Check that
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Let ƒ(x) = sin(x2) and I = ∫10 ƒ(x) dx.
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(a) Check that f'(x) = 2 cos(x²) - 4x² sin(x²). Then show that f"(x)| ≤ 6 for x = [0, 1]. 12 cos(x²)| ≤ 2 and 14x² sin(x²)| ≤ 4 for x € [0, 1]. 1 (b) Show that Error(MN) is at most 4N² (c) Find an N such that I - MN| ≤ 10-³.
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a Taking derivatives we get On the interval 0 1 fx 2x cosx fx 2x...View the full answer
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