Find max, min values of F(x) = int[1,x] f(t) dt for f(x) = min{x^3 + 1, 3 - x}

[provasanteriores]

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\(\displaystyle \mbox{3. Consider the function }\, f(x)\, =\, \min\{x^3\, +\, 1,\, 3\, -\, x\},\, F(x)\, =\, \)\(\displaystyle \displaystyle \int_1^x\, f(t)\, dt,\, \mbox{ where}\)

. . . . .\(\displaystyle \min\{p,\, q\}\, =\, \begin{cases}p&(\mbox{ if }\, p\, \leq\, q\,) \\q&(\mbox{ if }\, p\, >\, q\,) \end{cases}\)

\(\displaystyle \mbox{Find the maximal and the minimal value of }\, F(x).\)

 

[provasanteriores]

Integral simples

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http://imgur.com/MuMgMny

 

[Deleted member 4993]

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