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Chapter 7 Integrals Ex 7.6 Solutions

Question - 1 : -

xĀ sinĀ x

Answer - 1 : - LetĀ IĀ =Ā 

TakingĀ xĀ as first function and sinĀ xĀ assecond function and integrating by parts, we obtain

Question - 2 : -

Answer - 2 : - LetĀ IĀ =Ā 

TakingĀ xĀ as first function and sin 3xĀ assecond function and integrating by parts, we obtain

Question - 3 : -

Answer - 3 : - LetĀ 

TakingĀ x2Ā as first function andĀ exĀ assecond function and integrating by parts, we obtain

Again integrating by parts, we obtain

Question - 4 : -

xĀ logx

Answer - 4 : - LetĀ 

Taking logĀ xĀ as first function andĀ xĀ assecond function and integrating by parts, we obtain

Question - 5 : -

xĀ log 2x

Answer - 5 : - LetĀ 

Taking log 2xĀ as first function andĀ xĀ assecond function and integrating by parts, we obtain

Question - 6 : -

x2Ā logĀ x

Answer - 6 : - LetĀ 

Taking logĀ xĀ as first function andĀ x2Ā assecond function and integrating by parts, we obtain

Question - 7 : -

Answer - 7 : - LetĀ 

TakingĀ as first function andĀ xĀ as second function andintegrating by parts, we obtain

Question - 8 : -

Answer - 8 : - LetĀ 

TakingĀ Ā as first function andĀ xĀ as second function andintegrating by parts, we obtain

Question - 9 : -

Answer - 9 : - LetĀ 

Taking cosāˆ’1Ā xĀ as first function andĀ xĀ assecond function and integrating by parts, we obtain

Question - 10 : -

Answer - 10 : - LetĀ 

TakingĀ as first function and 1 as second function and integrating by parts, weobtain

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