InterviewSolution
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InterviewSolution
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फलन `f(x)=xg(x)` और `g(x)=[(1)/(x)]`, जहाँ `[*]`,अधिकतम पूर्णांक फलन है , पर विचार कीजिए । `int_(1//3)^(1)f(x)dx` किसके बराबर है ?A. `37//72`B. `2//3`C. `17//72`D. `37//144` |
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Answer» Correct Answer - A दिया है, f(x) =xg(x) तथा g(x) `=[(1)/(x)]`, तब, `f(x)=x[(1)/(x)]` दी गई सीमा को दो भागों में बाँटने पर , जब ,`((1)/(x)ltxlt(1)/(2))rArr2lt(1)/(x)lt3rArr[(1)/(x)]=2` `thereforef(x)=xg(x)=2x` जब `(1)/(2)ltxlt1` `rArr1lt(1)/(x)lt2rArr[(1)/(x)]=1` `thereforef(x)=xg(x)=x` अतः `f(x)={{:(2x","(1)/(3)lexlt(1)/(2),),(x","(1)/(2)lexlt1,):}` अब, `int_(1//3)^(1)f(x)dx=int_(1//3)^(1//2)2xdx+int_(1//2)^(1)xdx` `=2[(x^(2))/(2)]_(1//3)^(1//2)+[(x^(2))/(2)]_(1//2)^(1)` `=(2)/(2)[((1)/(2))^(2)-((1)/(3))^(2)]+(1)/(2)[(1)^(2)-((1)/(2))^(2)]` `=[(1)/(4)-(1)/(9)]+(1)/(2)[1-(1)/(4)]` `=(9-4)/(36)+(1)/(2)[(4-1)/(4)]=(5)/(36)+(3)/(8)` `=(10+27)/(72)=(37)/(72)` |
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