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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
The value of $\int\limits_{ - 7}^7 {\frac{{{5^x}}}{{{5^{[x]}}}}dx} $ is equal to (where $[.]$ denotes greatest integer function)
  • A
    $\frac {55}{ln\ 5}$
  • B
    $\frac {23}{ln\ 5}$
  • ✓
    $\frac {56}{ln\ 5}$
  • D
    $0$
✓

Answer

Correct option: C.
$\frac {56}{ln\ 5}$
c
$I = \int_{ - 7}^7 {{5^{x - [x]}}} dx = \int_{ - 7}^7 {{5^{\left[ x \right]}}} dx = 14\int_0^1 {{5^x}} dx$

$=14\left(\frac{5^{x}}{\ln 5}\right)_{0}^{1}=\frac{14}{\ln 5}(5-1)=\frac{56}{\ln 5}$

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