Question

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

• A. $a=3,b=-1$
• B. $a=3,b=1$
• C. $a=-3,b=1$
• D. $a=-3,b=-1$

Answer 1

The correct option is A $a=3,b=-1$

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 ${\int }_0^4(a\sqrt{x}+bx)dx=8$
$\Rightarrow \frac{2a}{3}[x^{\frac{3}{2}}{]}_0^4+\frac{b}{2}[x^2{]}_0^4=8,\frac{2a}{3}.8+8b=8$
$\Rightarrow 2a+3b=3$ …..(ii)
From equation (i) and (ii), we get $a=3,b=-1$ .