Definite Integration Question 45
Question 45
- 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:
- $\int_{0}^{\pi / 2} \sin x d x=\frac{\frac{\pi}{2}-0}{4} \sin 0+\sin \frac{\pi}{2}+2 \sin \frac{0+\frac{\pi}{2}}{2}$
$$ =\frac{\pi}{8}(1+\sqrt{2}) $$
