A) \[\sqrt{2}-1\]
B) \[\sqrt{2}\]
C) 1
D) \[\frac{1}{\sqrt{2}}\]
Correct Answer: A
Solution :
[a] IF \[={{e}^{-x}}\] \[\therefore y{{e}^{-x}}=\int{{{e}^{-x}}(cosx-sinx)dx}\] Put \[-x=t\] \[=-\int{{{e}^{t}}(cost+sint)dt=-{{e}^{t}}\sin t+c}\] \[y{{e}^{-x}}={{e}^{-x}}\sin x+c\] Since, y is bounded when \[x\to \infty \Rightarrow c=0\] \[\therefore y=\sin x\] Area \[=\int_{0}^{\pi /4}{(cosx-sinx)dx=\sqrt{2}}-1\]You need to login to perform this action.
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