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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int\limits_2^4 {\,\,\left[ {{{\log }_x}\,2\,\, - \,\,\frac{{{{\left( {{{\log }_x}\,2} \right)}^2}}}{{\ell n\,2}}} \right]} $ $dx =$
  • ✓
    $0$
  • B
    $1$
  • C
    $2$
  • D
    $4$
✓

Answer

Correct option: A.
$0$
a
$\int\limits_2^4 {\left( {\frac{{\ln \,2}}{{\ln x}}\,\, - \,\,\frac{{\ln 2}}{{{{\ln }^2}x}}} \right)} \,\,\,dx$     

$if $ $f(x) $ =$\frac{1}{{\ln \,x}}$

$ \Rightarrow \,\,\,x\,f\,'\,(x)\,\, = \,\, - \,\,\frac{1}{{{{\ln }^2}x}}$

$I = ln2 \left( {\frac{x}{{\ln x}}} \right)_2^4$=$\ln \,2\,\,\left[ {\frac{4}{{\ln 4}}\, - \,\frac{2}{{\ln 2}}} \right]$ = $ 0$

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