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Consider a quadratic $f(x)=ax^2+bx+c$ with unknown .What values of $a,b,c$ will minimise the integral $$ \int_0^1(f(x)-\frac{1}{1+x})^2?$$ How do I write in Mathematatica?Can Mathematica solve it exactly?Any \help \hint will be greatly appreciated.

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1 Answer 1

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Minimize[
 Integrate[(a*x^2 + b*x + c - 1/(1 + x))^2, {x, 0, 1}], {a, b, c}]
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    $\begingroup$ Add // Simplify and the result is cleaner. $\endgroup$
    – Bob Hanlon
    Oct 5 at 16:06

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