MCQ
જો $[x] $ એ મહતમ પૂર્ણાક છે , તો $\int_{\,1}^{\,5} {\,\,[|x - 3|]\,dx} =$
- A$1$
- ✓$2$
- C$4$
- D$8$
$ \Rightarrow I = \int_1^3 {[ - (x - 3)]\,dx + \int_3^5 {\,\left[ {(x - 3)} \right]} \,dx} $
$ \Rightarrow I = \int_1^2 {\,[ - (x - 3)} ]dx + \,\int_2^3 {\,[ - (x - 3)]dx + } \int_3^4 {[x - 3]\,dx }$${+ \int_4^5 {\,[x - 3]\,dx} } $
$ \Rightarrow I = \int_1^2 {\,dx} + \int_2^3 {0\,dx + \int_3^4 {0\,dx + \int_4^5 {\,dx} } } $
$ = [x]_1^2 + [x]_4^5$
$ \Rightarrow I = (2 - 1) + (5 - 4) = 2$.
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($I$) $f$ એ $\left(0, \frac{\pi}{2}\right)$ માં વધે છે
($II$) $f^{\prime}$ એ $\left(0, \frac{\pi}{2}\right)$ માં ઘટે છે