JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) bounded by the parabola \(y = x^2 -1\), the tangent at the point \((2, 3)\) into it and the \(y -\) axis is
- A \(\frac{8}{3}\)
- B \(\frac{32}{3}\)
- C \(\frac{53}{3}\)
- D \(\frac{14}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{8}{3}\)
Step-by-step Solution
Detailed explanation
Area \( = \int\limits_{ - 5}^3 x dy - \int\limits_{ - 1}^3 {xdy} \) \( = \int\limits_{ - 5}^3 {\left( {\frac{{y + 5}}{4}} \right)} - \int\limits_{ - 1}^3 {\sqrt {y + 1} dy} \) \(=\left|\frac{\frac{y^{2}}{2}+5 y}{4}\right|_{-5}^{3}-\left|\frac{2}{3}(y+1)^{3 / 2}\right|_{-1}^{3}\)…
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