MCQ
$\int_0^{\pi /2} {\frac{{\sin x\cos x}}{{1 + {{\sin }^4}x}}\,dx = } $
- A$\frac{\pi }{2}$
- B$\frac{\pi }{4}$
- C$\frac{\pi }{6}$
- ✓$\frac{\pi }{8}$
Now $\int_0^{\pi /2} {\frac{{\sin x\cos x}}{{1 + {{\sin }^4}x}}dx = \frac{1}{2}\int_0^1 {\frac{1}{{1 + {t^2}}}dt = \frac{1}{2}[{{\tan }^{ - 1}}t]_0^1 = \frac{\pi }{8}} } $.
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વિધાન $1 :$ $h(x) + h(-x) = 0$ $\forall x \in R$
વિધાન $2 :$ $h(x) + h(-x) = 2 \int\limits_0^x {g(t)dt} \forall x \in R$
વિધાન $3 :$ $h(3n) = 0 \forall n \in I$
તો આપેલ પૈકી ક્યાં વિધાન સત્ય છે ?