JEE Main & Advanced Mathematics Definite Integration Question Bank Area Bounded by Region, Volume and Surface Area of Solids of Revolution

  • question_answer If a curve \[y=a\sqrt{x}+bx\] passes through the point (1, 2) and the area bounded by the curve, line \[x=4\] and  x-axis is     8 sq. unit, then [MP PET 2002]

    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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