MCQ
$F(x) = \int_{{x^2}}^{{x^3}} {\frac{1}{{\log t}}\,dt} $ નું વિકલન મેળવો. $(x > 0)$
- A$\frac{1}{{3\log x}} - \frac{1}{{2\log x}}$
- B$\frac{1}{{3\log x}}$
- C$\frac{{3{x^2}}}{{3\log x}}$
- ✓${(\log x)^{ - 1}}.x(x - 1)$
$= \frac{{db}}{{dx}}f(b) - \frac{{da}}{{dx}}f(a)$
$a$ and $b$ are functions of $x.$
$\therefore \,\,\,F(x) = \int_{{x^2}}^{{x^3}} {\frac{1}{{\log t}}dt} $
==> $F'(x) = \frac{d}{{dx}}({x^3})\frac{1}{{\log {x^3}}} - \frac{d}{{dx}}({x^2})\frac{1}{{\log {x^2}}}$
$ = \frac{{3{x^2}}}{{3\log x}} - \frac{{2x}}{{2\log x}} = x(x - 1){(\log x)^{ - 1}}$.
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