This question is similar to Chapter 7 Class 12 Integrals - Ex 7.10

Please check the question here 

https://www.teachoo.com/4774/726/Ex-7.11--14---Using-properties--evaluate-integral-cos5-x-dx/category/Ex-7.11/

 

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Question 13 โˆซ_0^2๐œ‹โ€Šcosec^7 ๐‘ฅ ๐‘‘๐‘ฅ= (A) 0 (B) 1 (C) 4 (D) 2๐œ‹ โˆซ_0^2๐œ‹โ–’cosec^7โก๐‘ฅ ๐‘‘๐‘ฅ = โˆซ_0^2๐œ‹โ–’1/sin^7โก๐‘ฅ ๐‘‘๐‘ฅ =โˆซ_0^๐œ‹โ–’1/sin^7โก๐‘ฅ ๐‘‘๐‘ฅ+โˆซ_0^๐œ‹โ–’๐Ÿ/ใ€–๐’”๐’Š๐’ใ€—^๐Ÿ•โกใ€– (๐Ÿ๐… โˆ’ ๐’™)ใ€— ๐‘‘๐‘ฅ =โˆซ_0^๐œ‹โ–’1/sin^7โก๐‘ฅ ๐‘‘๐‘ฅ+โˆซ_0^๐œ‹โ–’๐Ÿ/(โˆ’๐’”๐’Š๐’ ๐’™)^๐Ÿ• ๐‘‘๐‘ฅ =โˆซ_0^๐œ‹โ–’1/sin^7โก๐‘ฅ ๐‘‘๐‘ฅโˆ’โˆซ_0^๐œ‹โ–’1/sin^7โก๐‘ฅ ๐‘‘๐‘ฅ = 0 So, the correct answer is (A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.