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Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

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Fill in the Blanks

Q.1. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE then A = ......., B = ....... and C = .......             (1990 -  2 Marks)

Ans.  Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE can have any real value.


Subjective Problems

Q. 1.  Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE            (1978)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 2.Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE        (1979)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
 

Q. 3. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE             (1981 - 2 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 4. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE             (1983 - 2 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 5. Evaluate the following Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE            (1984 - 2 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 6. Evaluate the following  Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                (1985 - 2½ Marks)

Ans.  Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 7. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE             (1987 - 6 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Q. 8. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                 (1989 - 3 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Put sin x – cos x = t ⇒ (cos x + sin x) dx = dt also (sin x – cos x)2 = t2 ⇒ 1 – sin 2x = t2\

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Q. 9. Find the indefinite integral Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE            (1992 -  4 Marks)

Ans.

  Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions.

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Thus we get the value of I on substituting the values of I1 and I2 from (2) and (3) in equation (1).


Q. 10. Find the indefinite integral Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE             (1994 -  5 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
∴ Integrating I with respect to θ, by parts we get

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 11. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                (1996 - 2 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 12. Integrate Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE                    (1999 - 5 Marks)

Ans.  Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Comparing and solving, we get,

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

where C is constant of integration.


Q. 13. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE            (2001 - 5 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEFill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE


Q. 14. For any natural number m, evaluate Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE               (2002 - 5 Marks)

Ans. Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Solutions. 

Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

The document Fill in the Blanks: Indefinite Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is a part of the JEE Course Maths 35 Years JEE Main & Advanced Past year Papers.
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