JEE  >  Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced

# Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

## Document Description: Integer Answer Type Questions: 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 Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced have been prepared according to the JEE exam syllabus. Information about Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced covers topics like and Integer Answer Type Questions: 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 Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced.

Introduction of Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced in English is available as part of our Maths 35 Years JEE Main & Advanced Past year Papers for JEE & Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced in Hindi for Maths 35 Years JEE Main & Advanced Past year Papers course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Integer Answer Type Questions: Definite Integrals and Applications of Integrals | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
 1 Crore+ students have signed up on EduRev. Have you?

Q. 1. Let f: R → R be a continuous function which satisfies            (2009) Then the value of f (ln 5) is                           (2009)

Ans. 0

Solution.  Integrating both sides with respect to x, we get Q. 2. For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [–10, 10] by Then the value of (2010)

Ans. 4

Solution. The graph of this function is as below Clearly f(x) is periodic with period 2

Also cos πx is periodic with period 2

∴ f ( x) cosπx is periodic with period 2  Q. 3. (JEE Adv. 2014)

Ans. 2

Solution.  Q. 4. Let f : R → R be a function defined by where [x] is the greatest integer less than or equal to x, if , then the value of (4I – 1) is            (JEE Adv. 2015)

Ans. 0

Solution. Also 0 < x2 < 1 ⇒ f(x2) = [x2] = 0
1 < x2 < 2 ⇒ f(x2) = [x2] = 1
2 < x2 < 3 ⇒ f(x2) = 0 (using definition of f)
3 < x2 < 4 ⇒ f(x2) = 0 (using definition of f)  Q. 5. Let for all x ∈ R and a continuous function. F or is the area of the region bounded by  x = 0, y = 0, y = f(x) and x = a, then f(0) is          (JEE Adv. 2015)

Ans. 3

Solution.   Q. 6. where tan–1x takes only principal values, then the value of is             (JEE Adv. 2015)

Ans. 9

Solution.  Q. 7. be a continuous odd function, which vanishes exactly at one point and f (1) = 1/2. Suppose that  then the value of (JEE Adv. 2015)

Ans. 7

Solution. f(t) being odd function

∴ Using L Hospital’s rule, we get Q. 8. The total number of distinct x ∈ [0, 1] for which (JEE Adv. 2016)

Ans. 1

Solution. ∴ f is decreasing on [0, 1]

Also f(0) = 1  ∴ f(x) crosses x-axis exactly once in [0, 1]

∴ f(x) = 0 has exactly one root in [0, 1]

The document Integer Answer Type Questions: Definite Integrals and Applications of 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.
All you need of JEE at this link: JEE

## Maths 35 Years JEE Main & Advanced Past year Papers

111 docs|70 tests
 Use Code STAYHOME200 and get INR 200 additional OFF

## Maths 35 Years JEE Main & Advanced Past year Papers

111 docs|70 tests

Track your progress, build streaks, highlight & save important lessons and more!

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;