JEE Mains · Maths · STD 12 - 8. Application and integration
The area (in sq. units) of the region \(\{(x,y):y^2 \geq 2x\,and\,x^2+y^2 \leq 4x,x \geq 0,y \leq 0 \}\) is
- A \(\pi - \frac{{4\sqrt 2 }}{3}\)
- B \(\frac{\pi }{2} - \frac{{2\sqrt 2 }}{3}\)
- C \(\;\pi - \frac{4}{3}\)
- D \(\;\pi - \frac{8}{3}\)
Answer & Solution
Correct Answer
(D) \(\;\pi - \frac{8}{3}\)
Step-by-step Solution
Detailed explanation
\( = \frac{{\pi {{\left( 2 \right)}^2}}}{4} - \sqrt 2 \int\limits_0^2 {\sqrt x dx} \) \(=\pi-\sqrt{2} \cdot \frac{2}{3} 2 \sqrt{2}\) \(=\pi-8 / 3\)
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