MCQ
વિધેય $y = ln^2x -1$ દ્વારા ચોથા ચરણમાં આવૃત પ્રદેશનું ક્ષેત્રફળ મેળવો.
- A$\frac{2}{e}$
- ✓$\frac{4}{e}$
- C$2\left( {e + \frac{1}{e}} \right)$
- D$4\left( {e - \frac{1}{e}} \right)$
$A=\left|\int_{1 / e}^{e}\left(\ln ^{2} x-1\right) d x\right|$
$\int\left(\ln ^{2} x-1\right) d x=\left(\ln ^{2} x\right) x-\int 2 \ln x \frac{1}{x} . x d x-x$
$=x\left(\ln ^{2} x\right)-x-2[x \ln x-x]$
$=x \ln ^{2} x-x-2 x \ln x+2 x$
$=x \ln ^{2} x+x-2 x \ln x$
$A=\left|\left[x \ln ^{2} x+x-2 x \ln x\right]^{e} 1 / e\right|=\left|e-\frac{1}{e}+e-1 / e-2[e+1 / e]\right|=|+4 / e|$
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