Question

The area 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 sq. units.

• A. $\frac{29}{24}$
• B. $\frac{37}{24}$
• C. $\frac{14}{3}$
• D. $\frac{187}{24}$

Answer 1

The correct option is B $\frac{37}{24}$


$y=x^2+1\Rightarrow m=4$
Eqn. of tangent is $y-5=4(x-2)$
$\Rightarrow y=4x-3$
$\therefore$ reqd. area $={\int }_0^2(x^2+1)dx-(\frac{1}{2}\times \frac{5}{4}\times 5)$
$=\frac{37}{24}$ sq. units.