JEE Mains · Maths · STD 12 - 8. Application and integration
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 \(\frac{8}{3}\)
- B \(\frac{37}{24}\)
- C \(\frac{187}{24}\)
- D \(\frac{14}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{37}{24}\)
Step-by-step Solution
Detailed explanation
Equation of tangent at \((2,5)\) is \(\frac{y+5}{2}=x(2)+1\) or \(y=4 x-3\) Required Area \( = \int\limits_0^2 {\left( {{x^2} + 1} \right)} dx - \frac{1}{2}\left( {2 - \frac{3}{4}} \right) \cdot (5)\) \(\left.=\frac{x^{3}}{3}+x\right]_{0}^{2}-\frac{25}{8}\)…
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