Error Estimate for Taylor Approx of Intergal(f(x)) from 0 to .5

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royzizzle
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explain why an estimate of intergal(f(x)) from 0 to .5 using the first 2 nonzero terms of its taylor approximation differs from the actual value of this integral by less than 1/200
 
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Why? I would think it pretty obvious but I would prefer to encourage you to do your own homework.