JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region \(\left\{ {x \in R:x \ge } \right.0,\,y \ge 0,\,y \ge x - 2\,and\,y \le \sqrt x \} \,,\,\) is
- A \(\frac{{13}}{3}\)
- B \(\frac{{10}}{3}\)
- C \(\frac{{5}}{3}\)
- D \(\frac{{8}}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{{10}}{3}\)
Step-by-step Solution
Detailed explanation
The intersection point of \(y=x-2\) and \(y=\sqrt{x}\) is \((4,2)\) Therequiredarea \(=\int_{0}^{4} \sqrt{x} d x-\frac{1}{2} \times 2 \times 2\) \(=\frac{16}{3}-2=\frac{10}{3}\)
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