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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
The function $L(x) = \int_1^x {\frac{{dt}}{t}} $ satisfies the equation
  • A
    $L(x + y) = L(x) + L(y)$
  • B
    $L\left( {\frac{x}{y}} \right) = L(x) + L(y)$
  • ✓
    $L(xy) = L(x) + L(y)$
  • D
    None of these
✓

Answer

Correct option: C.
$L(xy) = L(x) + L(y)$
c
(c) Given function $L(x) = \int_1^x {\frac{1}{t}dt = [\log t]_1^x} $

$= \log x - \log 1$

==> $L(x) = \log x$, 

Hence $L\,(xy) = L(x) + L(y)$.

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