Question

If a curve $y = a \sqrt { x } + b x$ 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.
• B. $a = 3 , b = 1$
• C. $a = - 3 , b = 1$
• D. $a = - 3 , b = - 1$

Answer 1

Answer: (A)

Answer 2

Given curve $y = a \sqrt { x } + b x$. 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 $\int _ { 0 } ^ { 4 } ( a \sqrt { x } + b x ) d x = 8$

⇒ $\frac { 2 a } { 3 } \left[ x ^ { 3 / 2 } \right] _ { 0 } ^ { 4 } + \frac { b } { 2 } \left[ x ^ { 2 } \right] _ { 0 } ^ { 4 } = 8$,

⇒ $2 a + 3 b = 3$ …..(ii)

From equation (i) and (ii), we get $a = 3 , b = - 1$.