SATHEE: Definite Integration Question 45

Definite Integration Question 45

Question 45

Good approximation of $\int_{0}^{π / 2} \sin x d x$ , is (a) $π / 4$ (b) $π (\sqrt{2} + 1) / 4$ (c) $π (\sqrt{2} + 1) / 8$ (d) $\frac{π}{8}$

Objective Questions II

(One or more than one correct option)

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Solution:

$\int_{0}^{π / 2} \sin x d x = \frac{\frac{π}{2} - 0}{4} \sin 0 + \sin \frac{π}{2} + 2 \sin \frac{0 + \frac{π}{2}}{2}$

$= \frac{π}{8} (1 + \sqrt{2})$

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