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Today's calculation of Integral 149

Source:

February 16, 2011
calculusintegrationcalculus computations

Problem Statement

Let f(x)=(1−x2)32f(x)=(1-x^2)^{\frac 32}. Denote MM the maximum value of ∣f′(x)∣|f'(x)| in (−1, 1)(-1,\ 1). Prove that ∫−11f(x) dx≤M.\int_{-1}^1 f(x)\ dx\leq M.
1981 Musashi Institute of Technology entrance exam/Electro Telecommunication, Civil Enginerring
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