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Question : 72 of 160
Marks:
+1,
-0
Solution:
We have,
∫(√1−sin‌x+√1+sin‌x)‌dx=f(x)+CLet
I=∫(√1−sin‌x+√1+sin‌x)‌dx=∫[|sin‌‌−cos‌|+|sin‌‌+cos‌|]‌dx=∫[(cos‌−sin‌‌)−(sin‌‌+cos‌)]‌dx‌‌[∵‌<x<‌⇒‌<‌<‌]=∫(cos‌−sin‌‌−sin‌‌−cos‌)‌dx=−2‌∫sin‌‌‌dx=4‌cos‌+CSo,
f(x)=4‌cos‌⇒f′(x)=−2sin‌‌f′(‌)=−2sin‌‌=−2×‌=√3
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