question_answer

The area of the region enclosed by the curves \[y=x\,\log \,x\] and \[y=2x-2{{x}^{2}}\] is

A)  \[\frac{7}{12}\]                               

B)  \[\frac{1}{2}\]

C)  \[\frac{5}{12}\]                               

D)  None of these

Correct Answer: A

Solution :

 Given curves are \[({{d}_{d}}g)t=2mv\times nt\] and \[\Rightarrow \]. Required area \[10\times 9.8=2\times 5\times v\times 10\] \[v=\frac{98}{100}=0.98\,m/s\] \[x={{(t-3)}^{2}}={{t}^{2}}-6t+9\] \[\Rightarrow \] \[v=\frac{dx}{dt}=2t-6\]