Home
Class 12
MATHS
For x epsilon(0,(5pi)/2), definite f(x)...

For `x epsilon(0,(5pi)/2)`, definite `f(x)=int_(0)^(x)sqrt(t) sin t dt`. Then `f` has

A

local maximum at `pi` an d `2pi`.

B

local minimum at `pi` an d `2pi`.

C

local maximum at `pi` and local maximum at `2pi`.

D

local maximum at `pi` and local minimum at `2pi`.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - I|49 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

For x in (0,(5pi)/2) , define f(x)""=int_0^xsqrt(t)sint"dt" Then f has : local maximum at pi and 2pi . local minimum at pi and 2pi local minimum at pi and local maximum at 2pi . local maximum at pi and local minimum at 2pi .

" If " f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is

If f(x)=x^(2)int_(0)^(1)f(t)dt+2 , then

If f(x) =int_(0)^(x) sin^(4)t dt , then f(x+2pi) is equal to

If f(x)=int_0^x(sint)/t dt ,x >0, then

If f(x)=int_0^x tf(t)dt+2, then

Let f(x) = int_(0)^(x)|2t-3|dt , then f is

If int_(0)^(x^(2)) sqrt(1+t^(2)) dt, then f'(x)n equals

Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

If f(x)=int_(0)^(x)|t-1|dt , where 0lexle2 , then

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - II
  1. Let p(x) be a function defined on R such that p'(x)=p'(1-x) for all x ...

    Text Solution

    |

  2. The area bounded by the curves y=cos x and y= sin x between the ordina...

    Text Solution

    |

  3. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

    Text Solution

    |

  4. Let [] denote the greatest integet function then the value int0^1.5 x[...

    Text Solution

    |

  5. The area of the region enclosed by the curve y=x, x=e,y=1/x and the po...

    Text Solution

    |

  6. Find the area of the region bounded by the curve y^(2)=4x" and " x^(2)...

    Text Solution

    |

  7. The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and ...

    Text Solution

    |

  8. If g(x) = int(0)^(x) cost dt, then g(x+pi) equals

    Text Solution

    |

  9. Statement I The value of the integral int(pi//6)^(pi//3) (dx)/(1+sqrt...

    Text Solution

    |

  10. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

    Text Solution

    |

  11. The integral int(0)^(pi)sqrt(1+4"sin"^(2)x/2-4"sin"x/2)dx is equals to...

    Text Solution

    |

  12. The area of the region described by A={(x,y):x^(2)+y^(2)le1 and y^(2)l...

    Text Solution

    |

  13. The integral int(2)^(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx is e...

    Text Solution

    |

  14. The area (in sq. units) of the region described by {x,y):y^(2)le2x and...

    Text Solution

    |

  15. The area (in sq. units) of the region {(x,y):y^(2) le 2x and x^(2)...

    Text Solution

    |

  16. lim(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n)is equal to

    Text Solution

    |

  17. The area (in sq. units) of the region {(x,y):xge0,x+yle3,x^(2) le4y} a...

    Text Solution

    |

  18. The Integral int(pi/4)^((3pi)/4)(dx)/(1+cosx) is equal to: ...

    Text Solution

    |

  19. The value of int(-pi//2)^(pi//2)(sin^(2)x)/(1+2^(x))dx is

    Text Solution

    |

  20. "Let "f(x)=cos x^(2),f(x)-sqrt(x), and alpha, beta (alphaltbeta) be th...

    Text Solution

    |