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Question : 77 of 160
Marks:
+1,
-0
Solution:
Let
I=∫| sin‌x−cos‌x |
| √sin‌2‌x |
.dx I=∫| sin‌x−cos‌x |
| √1+2‌sin‌x.cos‌x−1 |
dx I=∫| sin‌x−cos‌x |
| √(cos‌x+sin‌x)2−1 |
dx Let
sin‌x+cos‌x=t ⇒cos‌x−sin‌x= ⇒−(sin‌x−cos‌x)dx=dt ⇒(sin‌x−cos‌x)dx=−dt ∴I=−∫ [∵∫dx=log|x+√x2−a2|+C] =−log|t+√t2−1| =−log|sin‌x+cos‌x+√(sin‌x+cos‌x)2−1|+C I=−log|sin‌x+cos‌x+√sin‌2‌x|+C
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