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Chapter 7 Integrals Ex 7.6 Solutions

Question - 11 : -

Answer - 11 : - Let 

Taking  asfirst function and  as second function and integrating by parts, we obtain

Question - 12 : -

Answer - 12 : - Let 

Taking x as first function and sec2x assecond function and integrating by parts, we obtain

Question - 13 : -

Answer - 13 : - Let 

Taking  as first function and 1 as second function and integrating byparts, we obtain

Question - 14 : -

Answer - 14 : -

Taking  as first functionand x as second function and integrating by parts, we obtain

Again integrating by parts, we obtain

Question - 15 : -

Answer - 15 : - Let 

Let I = I1 + I2 …(1)

Where, and 

Taking log x asfirst function and x2 as second function andintegrating by parts, we obtain

Using equations (2) and(3) in (1), we obtain

Question - 16 : -

Answer - 16 : - Let 

Let
⇒ 
∴ 
It is known that, 

Question - 17 : -

Answer - 17 : - Let 

Let  ⇒ 
It is known that, 

Question - 18 : -

Answer - 18 : -

Let  ⇒ 
It is known that, 

From equation (1), weobtain

Question - 19 : -

Answer - 19 : -

Also, let  ⇒ 
It is known that, 

Question - 20 : -

Answer - 20 : -

Let  ⇒ 
It is known that, 

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