Question:
What is the area of the region enclosed in the first quadrant by \(x^2 + y^2 = \pi^2\), y = sin x and x = 0?
प्रथम चतुर्थांश में \(x^2 + y^2 = \pi^2\), y = sin x और x = 0 द्वारा परिबद्ध क्षेत्र का क्षेत्रफल क्या है?
Options:
- \(\dfrac{\pi^3}{2} – 1\)
- \(\dfrac{\pi^3}{4} – 2\)
- \(\dfrac{\pi^3}{4} – 1\)
- \(\dfrac{\pi^2}{4} – 2\)
- \(\dfrac{\pi^3}{2} – 1\)
- \(\dfrac{\pi^3}{4} – 2\)
- \(\dfrac{\pi^3}{4} – 1\)
- \(\dfrac{\pi^2}{4} – 2\)
Correct Answer: c)
Explanation:
Area in the first quadrant bounded by \(x^2 + y^2 = \pi^2\), \(y = \sin x\) and \(x = 0\) evaluates to \(\dfrac{\pi^3}{4} – 1\).
प्रथम चतुर्थांश में वक्रों द्वारा परिबद्ध क्षेत्र का समाकलन करने पर \(\dfrac{\pi^3}{4} – 1\) प्राप्त होता है।