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The area (in sq. units) in the first quadrant bounded by the parabola,

Question:

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

  1. $\frac{14}{3}$

  2. $\frac{187}{24}$

  3. $\frac{37}{24}$

  4. $\frac{8}{3}$

Correct Option: , 3

Solution:

Area $=\int_{0}^{2}\left(x^{2}+1\right) d x-\frac{1}{2}\left(\frac{5}{4}\right)(5)=\frac{37}{24}$

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