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# Fill in the Blanks: Definite Integrals and Applications of Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

## Document Description: Fill in the Blanks: Definite Integrals and Applications of Integrals | JEE Advanced for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The notes and questions for Fill in the Blanks: Definite Integrals and Applications of Integrals | JEE Advanced have been prepared according to the JEE exam syllabus. Information about Fill in the Blanks: Definite Integrals and Applications of Integrals | JEE Advanced covers topics like and Fill in the Blanks: Definite Integrals and Applications of Integrals | JEE Advanced Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Fill in the Blanks: Definite Integrals and Applications of Integrals | JEE Advanced.

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Q. 1.

(1987 - 2 Marks)

Ans.

Solution. Given that,

Expanding along R1, we get

Multiply the above by π/2 when n is even. We get

Q. 2.                (1988 - 2 Marks)

Where [ ] denotes the greatest integer function, equals .......

Ans. 2 - √2

Solution.

Q. 3.                 (1989 - 2 Marks)

Ans. 4

Solution.

Q. 4.                 (1993 -  2 Marks)

Ans.

Solution.

Q. 5.                    (1994 -  2 Marks)

Ans. 1/2

Solution.

Adding (1) and (2), we get

Q. 6. If for nonzero   then               (1996 - 2 Marks)

Ans.

Solution.               …(1)

Integrating both sides within the limits 1 to 2, we get

Replacing

Integrating both sides within the limits 1 to 2, we get

Eliminate   between (2) and (3) by multiplying (2) by a and (3) by b and subtracting

Q. 7.               (1996 - 1 Mark)

Ans. π2

Solution.

…(2)

Adding (1) and (2) we get

… (3)

[ Using above property again]

....(4)

Adding (3) and (4) we get

Q. 8. The value of                    (1997 - 2 Marks)

Ans. 2

Solution.

Q. 9. then one of the possible values of k is .......                 (1997 - 2 Marks)

Ans. 16

Solution.

True / False

Q. 1. The value of the integral equal to a.             (1997 - 2 Marks)

Ans. T

Solution.

… (1)

… (2)
Adding (1) and (2), we get

∴ The given statement is true.

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