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Question : 77 of 160
Marks:
+1,
-0
Solution:
∫| sec‌x |
| √sin(2x+θ)+sin‌θ |
dx=I (say)
I=∫| sec‌x |
| √sin‌2‌x‌cos‌θ+cos‌2‌x‌sin‌θ+sin‌θ |
dx I=∫| sec‌x |
| √sin‌2‌x‌cos‌θ+(cos‌2‌x+1)‌sin‌θ |
dx =∫| secx |
| √2‌cos‌x(sin‌x‌cos‌θ+cos‌x‌sin‌θ) |
dx [∵cos‌2‌x+1=2cos2x]
=∫| sec‌x |
| √2cos2x‌cos‌θ(tan‌x+tan‌θ) |
dx =‌∫dx Let
tan‌x+tan‌θ=u ⇒sec2xdx=du =‌∫=.2.√u+c =.√tan‌x+tan‌θ+c =√| 2(tan‌x+tan‌θ) |
| cos‌θ |
+c =√2(tan‌x+tan‌θ)‌sec‌θ+c
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