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Algebra
Question

Find the value of the constant \(a\) for which th...

Find the value of the constant \(a\) for which the function \(f ( x ) = a x ^ { 2 }\) best approximates the function \(g ( x ) = x ^ { 3 }\) on the interval \([ 0,1 ]\) , in the sense that the integral \(I = \int _ { 0 } ^ { 1 } ( f ( x ) - g ( x ) ) ^ { 2 } d x\)

Answer

\(a = 5 / 6 , I = 1 / 252\)

Solution
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