Indefinite Integration 1 Question 45
46. Good approximation of $\int _0^{\pi / 2} \sin x d x$, is
(a) $\pi / 4$
(b) $\pi(\sqrt{2}+1) / 4$
(c) $\pi(\sqrt{2}+1) / 8$
(d) $\frac{\pi}{8}$
Objective Questions II
(One or more than one correct option)
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Solution:
- $\int _0^{\pi / 2} \sin x d x=\frac{\frac{\pi}{2}-0}{4} \sin 0+\sin \frac{\pi}{2}+2 \sin \frac{0+\frac{\pi}{2}}{2}$
$$ =\frac{\pi}{8}(1+\sqrt{2}) $$
