defence exam Coast Guard Navik GD (General Duty) 02/2025 Mock Test Series Mathematics Integral Calculus Application of Integrals
The area enclosed in the region
{(x, y) : x2 + y2 ≤ 1 ≤ x + \(\frac{y}{2}\) }
(in sq. units) is
1
\(\frac{{\rm{\pi }}}{{\rm{4}}}\,{\rm{ + }}\,\frac{{\rm{2}}}{{\rm{25}}}\, - \,\frac{1}{2}{\sin ^{ - 1}}\frac{3}{5}\)
2
\(\frac{{\rm{\pi }}}{{\rm{4}}}\,{\rm{ - }}\,\frac{{\rm{2}}}{{\rm{25}}}\, - \,\frac{1}{2}{\sin ^{ - 1}}\frac{3}{5}\)
3
\(\frac{{\rm{\pi }}}{{\rm{4}}}\,{\rm{ + }}\,\frac{{\rm{2}}}{{\rm{25}}}\, + \,\frac{1}{2}{\cos ^{ - 1}}\frac{3}{5}\)
4
\(\frac{{\rm{\pi }}}{{\rm{4}}}\,{\rm{ - }}\,\frac{{\rm{2}}}{{\rm{25}}}\, - \,\frac{1}{2}{\cos ^{ - 1}}\frac{3}{5}\)