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 CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|36 Videos
  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|75 Videos
  • DIFFERENTIAL EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCE (ARCHIVE )|32 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 CALCULUS 2-JEE Advanced (Archive)
  1. The set of all x for which log(1+ x) le x is equal to …… .

    Text Solution

    |

  2. The function y=2x^2-log(x) is monotonically increasing for values of x...

    Text Solution

    |

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

    Text Solution

    |

  4. Using the relation 2(1−cosx)<x^2 ,x=0 or prove that sin(tanx)≥x,∀ϵ[0,...

    Text Solution

    |

  5. Let -1leple1, show that the equation 4x^(3)-3x-p=0 has a unique root i...

    Text Solution

    |

  6. Let f(x)={{:(xe^(ax)",", x le0),(x+ax^2-x^3",",x gt 0):} where a is po...

    Text Solution

    |

  7. Show that 2sinx+tanx≥3x, where 0≤x< π/2 ​

    Text Solution

    |

  8. Show that 1+xin(x+sqrt(x^2+1))geqsqrt(1+x^2) for all xgeq0.

    Text Solution

    |

  9. For a twice differentiable function f(x),g(x) is defined as g(x)=f^(pr...

    Text Solution

    |

  10. For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...

    Text Solution

    |

  11. Find a point on the curve x^(2)+2y^(2)=6 whose distance from the line ...

    Text Solution

    |

  12. Suppose f(x) is a function satisfying the folowing conditions: (i)f(...

    Text Solution

    |

  13. Let S be a square of unit area. Consider any quadrilateral which has o...

    Text Solution

    |

  14. Determine the point of maxima and minima of the function f(x)=1/8(log)...

    Text Solution

    |

  15. Let (h , k) be a fixed point, where h >0,k > 0. A straight line passin...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. Which normal to the curve y=x^(2) forms the shortest chord?

    Text Solution

    |

  18. A window of perimeter P (including the base of the arch) is in the ...

    Text Solution

    |

  19. A point P is given on the circumference of a circle of radius r. Chord...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |