If a curve `y =a sqrtx+bx` passes through point `(1,2)` and the area bounded by curve, line `x=4` and x-axis is 8, then : (a) `a=3` (b) `b=3` (c) `a=-1` (d) `b=-1`

Options

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

Answer

A

Explanation

It is given that `y=asqrtx+bx` passes through the point (1,2).
`therefore2=a+b" "...(i)`
It is given that
`underset(0)overset(4)(int)(asqrtx+bx)dx=8`
`implies[(2)/(3)ax^(3//2)+b/2x^(2)]_(0)^(4)=8`
`implies16/3a+8b=8implies2/3a+b=1" "...(ii)`
Solving (i)and (ii), we get `a=3, b=-1.`