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If the curve y=a x^(1/2)+b x passes thro...

If the curve `y=a x^(1/2)+b x` passes through the point `(1,2)` and lies above the x-axis for `0lt=xlt=9` and the area enclosed by the curve, the x-axis, and the line `x=4` is `8` sq. units, then (a)`a=1` (b) `b=1` `a=3` (d) `b=-1`

A

`a=1`

B

`b=1`

C

`a=3`

D

`b=-1`

Text Solution

Verified by Experts

The correct Answer is:
C, D
Since the curve `y=ax^(1//2)+bx` passes through the point (1,2)
`therefore" "2=a+b" (1)"`
By observation the curve also passes through (0,0). Therefore, the area enclosed by the curve, x-axis and x=4 is given by
`A=overset(4)underset(0)int(ax^(1//2)+bx)dx=8 or (2a)/(3)xx8+(b)/(2)xx16=8`
`or (2a)/(3)+b=1." (2)"`
Solving (1) and (2), we get a =3, b=-1.
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