Home
Class 12
MATHS
Prove that for x in [0, (pi)/(2)], sin x...

Prove that for `x in [0, (pi)/(2)], sin x + 2x ge (3x(x + 1))/(pi)`.

Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE MAIN (ARCHIVE )|28 Videos

  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos

Similar Questions

Explore conceptually related problems

"For x " in (0,(pi)/(2)) , "Prove that sin "x gt x -(x^(2))/(6)

Prove that : int_(0)^(pi//2) (sin x -cos x) log (sin^(3) x + cos^(3)x) dx=0

Prove that int_0^(pi/2) \ sin^2 x / (1+sin x cos x) \ dx = pi/(3 sqrt(3)

Prove that : int_(0)^(pi//2) (sin x-cos x)/(1+sin x cos x)dx=0 " (ii) Prove that " : int_(0)^(pi//2) sin 2x. log (tan-x) dx=0

Prove that : int_(0)^(pi) (x sin x)/(1+cos^(2)x) dx =(pi^(2))/(4)

Prove that : int_(0)^(pi) sin^(2m) x. cos^(2m+1) x dx=0

Prove that :int_(0)^(pi) (x)/(1 +sin^(2) x) dx =(pi^(2))/(2sqrt(2))

Prove that : int_(0)^(pi//2) (sin^(3)x)/(sin^(3) x+ cos^(3)x)dx =(pi)/(4)

Consider f(x)=sin3x,0<=x<=(pi)/(2), then (a) f(x) is increasing for x in(0,(pi)/(6)) and decreasing for x in((pi)/(6),(pi)/(2)) (b) f(x) is increasing forx in(0,(pi)/(4)) and decreasing for x in((pi)/(4),(pi)/(2)) (c) f(x)

Prove that : int_(0)^(pi) (x sin x)/(1+sinx) dx=pi((pi)/(2)-1)

VMC MODULES ENGLISH-DIFFERENTIAL EQUATIONS-JEE ADVANCE (ARCHIVE )
  1. The differential equation representing the family of curves y^2=2c(...

    Text Solution

    |

  2. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

    Text Solution

    |

  3. Prove that for x in [0, (pi)/(2)], sin x + 2x ge (3x(x + 1))/(pi).

    Text Solution

    |

  4. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

    Text Solution

    |

  5. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  6. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

    Text Solution

    |

  7. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

    Text Solution

    |

  8. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |

  9. The function y=f(x) is the solution of the differential equation (d...

    Text Solution

    |

  10. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

    Text Solution

    |

  11. Let the f (x) be differentiabe function on the interval (0,oo) such ...

    Text Solution

    |

  12. Integrating factor of sec^2y dy/dx+x tany=x^3

    Text Solution

    |

  13. Let u(x) and v(x) be two continous functions satisfying the different...

    Text Solution

    |

  14. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

    Text Solution

    |

  15. A curve passes through the point (1,pi/6) . Let the slope of the curve...

    Text Solution

    |

  16. Tangent is drawn at any point P of a curve which passes through (1, 1...

    Text Solution

    |

  17. A spherical rain drop evaporates at a rate proportional to its surf...

    Text Solution

    |

  18. If length of tangent at any point on the curve y=f(x). Intercepted bet...

    Text Solution

    |

  19. A right circular cone with radius R and height H contains a liquid whi...

    Text Solution

    |

  20. A country has a food deficit of 10%. Its population grows continuously...

    Text Solution

    |