Home
Class 12
MATHS
Let F(x) be an indefinite integral of si...

Let F(x) be an indefinite integral of `sin^(2)x`
Statement-1: The function F(x) satisfies `F(x+pi)=F(x)` for all real x. because
Statement-2: `sin^(3)(x+pi)=sin^(2)x` for all real x.
A) Statement-1: True , statement-2 is true, Statement -2 is not a correct explanation for statement -1
c) Statement-1 is True, Statement -2 is False.
D) Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

d
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    RESONANCE|Exercise PART-II JEE MAIN|8 Videos
  • INDEFINITE INTEGRATION

    RESONANCE|Exercise HIGH LEVEL PROBLEMS (HLP)|29 Videos
  • INDEFINITE INTEGRATION

    RESONANCE|Exercise COMPREHENSION|1 Videos
  • GEOMETRY

    RESONANCE|Exercise Exercise-1 (Part-I: Previous Asked Question For Pre RMO)|50 Videos
  • MATRICES & DETERMINANT

    RESONANCE|Exercise HLP|33 Videos

Similar Questions

Explore conceptually related problems

Let F(x) be an indefinite integral of sin^(2)x Statement I The function F(x) satisfies F(x+pi)=F(x) for all real x. Because Statement II sin^(2)(x+pi)=sin^(2)x, for all real x. (A) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I. (B)Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I. (C) Statement I is true, Statement II is false. (D) Statement I is false, Statement II is ture.

Let F(x) be an indefinite integral of sin2x . Statement- 1: The function F(x) satisfies F(x+pi)=F(x) for all real x . Statement- 2: sin2(x+pi)=sin2x for all real x . (A) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I. (B)Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I. (C) Statement I is true, Statement II is false. (D) Statement I is false, Statement II is ture.

Consider the function F(x)=intx/((x-1)(x^2+1))dx Statement-1: F(x) is discontinuous at x=1 ,Statement-2: Integrand of F(x) is discontinuous at x=1 (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Statement-1: The function F(x)=intsin^2xdx satisfies F(x+pi)=F(x),AAxinR ,Statement-2: sin^2(x+pi)=sin^2x (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-x)) . Statement-1: f(c)""=1/3, for some c in R . Statement-2: 0""<""f(x)lt=1/(2sqrt(2)), for all x in R . (1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1 (2) Statement-1 is true, Statement-2 is false (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Statement-1: intsin^-1xdx+intsin^-1sqrt(1-x^2)dx=pi/2x+c Statement-2: sin^-1x+cos^-1x=pi/2 (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1. (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1. (C) Statement-1 is True, Statement-2 is False. (D) Statement-1 is False, Statement-2 is True.

Each question has 5 choices (a) ,(b) ,(c ) (d) and (e ) out of which ONLY ONE is correct. (a) Statement -1 is True, Statement -2 is True , Statement -2 is a correct explanation for Statement -1. (b) Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statement -1. (C ) Statement -1 is True, Statement -2 is False. (d) Statement -1 is False, Statement -2 is True. (e) Statement -1 and Statement -2 both are False. Statement -1: Yield of R-Br follows the order 1^(@) gt 2^(@) gt 3^(@) in Hundsdicker reaction Statement -2: Hundsdicker reaction follows free redical mechanism.

Each question has 5 choices (a) ,(b) ,(c ) (d) and (e ) out of which ONLY ONE is correct. (a) Statement -1 is True, Statement -2 is True , Statement -2 is a correct explanation for Statement -1. (b) Statement -1 is True, Statement -2 is True, Statement -2 is NOT a correct explanation for Statement -1. (C ) Statement -1 is True, Statement -2 is False. (d) Statement -1 is False, Statement -2 is True. (e) Statement -1 and Statement -2 both are False. Statement -1: Statement -2: Migratory aptitude of p-methoxyphenyl group is greater than migratory aptitude p-nitrophenyl of group during carbrocation rearrangements.