Question-135544

Question Number 135544 by 0731619177 last updated on 13/Mar/21

Answered by Olaf last updated on 13/Mar/21

f (x) = \sin x + \cos x = \sqrt{2} \cos (\frac{π}{4} - x)

x \in [0, \frac{π}{4}] \Rightarrow f (x) \in [1, \sqrt{2}]

\Rightarrow \forall x \in [0, \frac{π}{4}] ⌊ f (x) ⌋ = 1

Ω = \int_{0}^{\frac{π}{4}} \cos (2 x) \times 2^{1} d x

Ω = {[\sin (2 x)]}_{0}^{\frac{π}{4}} = 1

Commented by 0731619177 last updated on 13/Mar/21

t h a n k s