A) remains constant
B) becomes more than two times
C) becomes half
D) becomes less than two times
Correct Answer: D
Solution :
\[I.F={{e}^{\int_{{}}^{{}}{\frac{g'(x)}{g(x)}dx}}}={{e}^{\ln g(x)}}=g(x)\] When V is halved, \[\Rightarrow \,y.g(x)=\frac{1}{2}\,\int_{{}}^{{}}{\frac{2g(x)g'(x)}{1+{{g}^{2}}(x)}\,dx=\frac{1}{2}}\] remains the same but\[\ell n\,(1+{{g}^{2}}(x))+C\] becomes two times \[C=1-\frac{\ell n\,2}{2}\] \[\therefore \,\,\,y(e)\,.g(e)=\frac{1}{2}\,\ell n\,\,(1+2e-1)+1-\frac{\ell n2}{2}\,=\frac{3}{2}\]
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