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Question Number 167473 by mnjuly1970 last updated on 17/Mar/22

$$$$$$solve$$$$$$$${\int }_2^3\lfloor x^2-2x+5\rfloor dx=?$$$$$$

Answered by MJS_new last updated on 17/Mar/22

$$f\left(x\right)=\lfloor x^2-2x+5\rfloor$$$$f\left(x\right)=5;2⩽x<1+\sqrt{2}$$$$f\left(x\right)=6;1+\sqrt{2}⩽x<1+\sqrt{3}$$$$f\left(x\right)=7;1+\sqrt{3}⩽x<3$$$$\Rightarrow$$$$\mathrm{answer}\mathrm{is}9-\sqrt{3}-\sqrt{2}$$

Commented by mnjuly1970 last updated on 17/Mar/22

$$grateful$$

Answered by mathman1234 last updated on 17/Mar/22

$${\int }_2^3({\mathrm{x}}^2-2\mathrm{x}+5)\mathrm{dx}={[\frac{{\mathrm{x}}^3}{3}-{\mathrm{x}}^2+5\mathrm{x}]}_2^3$$$$=(9-9+15)-(\frac{8}{3}-4+10)$$$$=\frac{19}{3}$$

Commented by mr W last updated on 17/Mar/22

$$\lfloor {\mathrm{x}}^2-2\mathrm{x}+5\rfloor \ne ({\mathrm{x}}^2-2\mathrm{x}+5)$$

Commented by mnjuly1970 last updated on 18/Mar/22

$$✓$$

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