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Question : 77 of 160
Marks:
+1,
-0
Solution:
I=dx ...(i) ⇒I=| cos2022(−X) |
| 1+(2022)−x |
dx ...[∵f(a+b−x)dx=f(x)dx] I=| cos2022x.(2022)x |
| (2022)x+1 |
dx ...(ii) On adding
Eqs(i)‌and(ii) 2I=coss2022xdx ⇒2I=2‌cos2022xdx ...[∵cos‌x2022‌is‌an‌even‌function] ∴I=cos2022xdx=2‌cos2022xdx 2‌2022C1011 ...[∵cos2nxdx=.‌2nCn] =⋅=| π⋅2022! |
| 22022((1011)!)2 |
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