MCQ
$\int_0^{\pi /2} {\sin x\,\sin 2x} =$
- A$\frac{4}{3}$
- B$\frac{1}{3}$
- C$\frac{3}{4}$
- ✓$\frac{2}{3}$
$= 2\int_0^{\pi /2} {{{\sin }^2}x\cos xdx} $
Put $t = \sin x \Rightarrow dt = \cos x\,dx$
Now, $I = 2\int_0^1 {{t^2}dt = \frac{2}{3}[{t^3}]_0^1 = \frac{2}{3}} $.
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$f(x)=(1+|\sin x|)^{\frac{3 a}{\sin x \mid}} ,\quad -\frac{\pi}{4}\,<\,x\,<\,0$
$\quad\quad\quad\quad\quad\quad b ,\quad\quad\quad\quad\quad x=0$
$\quad\quad\quad\quad e^{\cot 4 x / \cot 2 x} ,\quad\quad\quad 0\,<\,x\,<\,\frac{\pi}{4}$
જો $\mathrm{f}$ એ $\mathrm{x}=0$ આગળ સતત હોય તો $6 \mathrm{a}+\mathrm{b}^{2}$ ની કિમંત મેળવો.