defence exam Coast Guard Navik GD (General Duty) 02/2025 Mock Test Series Mathematics Integral Calculus Indefinite Integrals
If \(\int {f\left( x \right).\sin x\cos x\,dx = \frac{1}{{2\left( {{b^2} - {a^2}} \right)}}.\log \left( {f\left( x \right)} \right) + c} \), then f(x) is
1
\(\frac{1}{{{a^2}{{\sin }^2}x + {b^2}{{\cos }^2}x} + k}\), ,
2
\(\frac{1}{{{a^2}{{\sin }^2}x - {b^2}{{\cos }^2}x}+ k}\)
3
\(\frac{1}{{a{{\cos }^2}x + b{{\sin }^2}x}}\)
4
None