A) \[a=3,\,b=-1\]
B) \[a=3,\,b=1\]
C) \[a=-3,\,b=1\]
D) \[a=-3,\,b=-1\]
Correct Answer: A
Solution :
Given curve \[y=a\sqrt{x}+bx\]. This curve passes through (1, 2), \[\therefore 2=a+b\] ?..(i) and area bounded by this curve and line \[x=4\] and x-axis is 8 sq. unit, then \[\int_{\,0}^{\,4}{(a\sqrt{x}+bx)\,}dx=8\] Þ \[\frac{2a}{3}[{{x}^{3/2}}]_{0}^{4}+\frac{b}{2}[{{x}^{2}}]_{0}^{4}=8\], \[\frac{2a}{3}.8+8b=8\] Þ \[2a+3b=3\] ?..(ii) From equation (i) and (ii), we get \[a=3,\,b=-1\].
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