question_answer

If A is the area of the region bounded by the curve \[y=\sqrt{3x+4},\] x-axis and the lines \[x=-1\]and \[x=4\]and B is that area bounded by curve \[{{y}^{2}}=3x+4,\]x axis and the lines \[x=-1\]and \[x=4,\] then \[A:B\]is equal to

A)  \[1:1\]         

B)  \[2:1\]

C)  \[1:2\]         

D)  None of these

Correct Answer: B

Solution :

Given, area bounded by the curve, \[y=\sqrt{3x+4},\] x-axis and the line \[x=-1\] and \[x=4\] is A and area bounded by the curve \[{{y}^{2}}=3x+4\] \[\Rightarrow \] \[y=\pm {{(3x+4)}^{1/2}}\] x-axis and the line \[x=-1\] and \[x=4\] is B. \[\therefore \] \[B=2A\] (Since, it is the area of both sides about x-axis] Now,  \[A:B=A:2\,\,\,\,A=1:2\]