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The area (in square units) of the region...

The area (in square units) of the region bounded by `y = sqrt(x), x ge 0` tangent to it at `(4,2)` & x-axis is :

A

`16/3`

B

`2/3`

C

`8/3`

D

`32/3`

Text Solution

Verified by Experts

The correct Answer is:
C
`(dy)/(dx) = 1/(2sqrt(x)) = 1/4 at (4/2)`
Equation of tangent is `x - 4y + 4 = 0`
shaded area = `1/2 xx 8 xx 2 - int_(0)^(4) sqrt(x) dx = 8 - |2/3 x^(3//2)|_(0)^(4) = 8 - 2/3 codt 4.2 = 8/3` square units.
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