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The area (in sq. units) in the first qua...

The area (in sq. units) in the first quadrant bounded by the parabola `y=x^2+1`, the tangent to it at the point (2, 5) and the coordinate axes is

A

`37/24`

B

`14/3`

C

`8/3`

D

`187/24`

Text Solution

Verified by Experts

The correct Answer is:
A
Equation of tangent to the parabola `y = x^(2) +1 at (2,5) is 4x -y -3 =0`
Required Area
`= int _(0)^(2) (x ^(2) +1) dx -1/2 xx 5/4 xx5`
`= (x ^(3))/(3 ) + x ]_(0)^(2) - (25)/(8) =14/3 -25/8 =37/24`
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