MCQ
$\int\limits_{ - 3\pi }^{3\pi } {{{\sin }^2}\,\theta {\mkern 1mu} si{n^2}\,2\,\theta d\theta } $ is equal to
- A$\pi $
- ✓$\frac{{3\pi }}{2}$
- C$\frac{{5\pi }}{2}$
- D$6\pi $
$=8 \int_{0}^{3 \pi} \sin ^{4} \theta \cos ^{2} \theta \mathrm{d} \theta=24 \int_{0}^{\pi} \sin ^{4} \theta \cos ^{2} \theta \mathrm{d} \theta$
$=48 \int_{0}^{\pi / 2} \sin ^{4} \theta \cos ^{2} \theta d \theta$
$=\frac{48 \cdot(3.1) \cdot(1)}{6.4 \cdot 2} \cdot \frac{\pi}{2}=\frac{3 \pi}{2}$
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$STATEMENT -1$ : For each real $\mathrm{t}$, there exists a point $\mathrm{c}$ in $[\mathrm{t}, \mathrm{t}+\pi]$ such that $\mathrm{f}^{\prime}(\mathrm{c})=0$. because
$STATEMENT -2$: $f(t)=f(t+2 \pi)$ for each real $t$.