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Question Number 206613 by hardmath last updated on 20/Apr/24

$$\mathrm{If}\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}{\mathrm{x}}^2,\mathrm{x}⩽2\\ \mathrm{f}(\mathrm{x}-3),\mathrm{x}>2\end{array}$$$$\mathrm{Find}{\int }_{-1}^{53}\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=?$$

Answered by MM42 last updated on 20/Apr/24

$$57$$

Answered by MM42 last updated on 22/Apr/24

$$\mathrm{\forall }-1⩽x⩽2\mathrm{\&}2<x⩽5\mathrm{\&}5<x⩽8\mathrm{\&}...50<x⩽53$$$$\Rightarrow f\left(x\right)=x^2;for18terms$$$$\Rightarrow {\underset{-1}{\int }}^{53}f\left(x\right)dx=18{\int }_{-1}^2{x}^{2}dx=54✓$$$$$$

Commented by MM42 last updated on 21/Apr/24

Commented by Tinku Tara last updated on 20/Apr/24

$$2+17\times 3=53$$$$\mathrm{Total}18\mathrm{terms}.\mathrm{Not}19$$

Commented by MM42 last updated on 21/Apr/24

$$ok.thanks$$

Commented by hardmath last updated on 22/Apr/24

$$\mathrm{cool}\mathrm{dear}\mathrm{professor}\mathrm{thank}\mathrm{you}$$

Commented by MM42 last updated on 23/Apr/24

$$\underset{―}{\underbrace{⋚}}$$

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