Home
Class 12
MATHS
The least value of the function phi(x)=i...

The least value of the function `phi(x)=int_((7pi)/6)^(x)(4sint+3cost)dt` on the interval `[(7pi)/6,(4pi)/3]` is

A

`(sqrt(3)+1)/2`

B

`(sqrt(3)-1)/2`

C

`(7(1-sqrt(3)))/2`

D

`-((sqrt(3)+1)/2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise COMPETITIVE THINKING|148 Videos

  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos

  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

The least value of the function phi(x)=int_(5pi//4)^(x) (3sin t+4 cos t)dt on the integral [5pi//4,4pi//3] , is

The least value of the function phi(x)=int_(5 pi/4)^(x)(3sin t+4cos t)dt on the interval [5 pi/4,4 pi/3] is (i) sqrt(3)+(3)/(2)( ii) -2sqrt(3)+(3)/(2)+(1)/(sqrt(2))( iii) (3)/(2)+(1)/(sqrt(2))( iv) none of these

The greatest value of f(x)=int_((5 pi)/(3))^(x)(6cos t-2sin t)dt in the interval [(5 pi)/(3),(7 pi)/(4)], is equal to

The maximum value of the function f(x)=sin(x+(pi)/(6))+cos(x+(pi)/(6)) in the interval (0,(pi)/(2)) occurs at (pi)/(12) (b) (pi)/(6)(c)(pi)/(4)(d)(pi)/(3)

int_(pi/6)^( pi/3)sin(3x)dx

Find the maximum value of F(x)=int_((7 pi)/6)^(x)(a sin t+b cos t)dt,a,b in R^(+),x in[(7 pi)/(6),sqrt(21)] is

STATEMENT 1 : On the interval [(5pi)/4,(4pi)/3]dot the least value of the function f(x)=int_((5x)/4)^x(3sint+4cost)dti s0 STATEMENT 2 : If f(x) is a decreasing function on the interval [a , b], then the least value of f(x) is f(b)dot

TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST
  1. Let f(x)=(e^(x)+1)/(e^(x)-1) and int(0)^(1) x^(3) .(e^(x)+1)/(e^(x)-1)...

    Text Solution

    |

  2. If m and n are positive integers and f(m,n)=int(0)^(1)x^(n-1)(logx)^(m...

    Text Solution

    |

  3. The least value of the function phi(x)=int((7pi)/6)^(x)(4sint+3cost)dt...

    Text Solution

    |

  4. Prove that int(a)^(b)f(x)dx=(b-a)int(0)^(1)f((b-a)x+a)dx

    Text Solution

    |

  5. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  6. If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x...

    Text Solution

    |

  7. lim(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+2))+sqrt(n/(n+3))+………..+sqrt(n...

    Text Solution

    |

  8. lim(n->oo)sum(n=1)^n(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^2)

    Text Solution

    |

  9. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

    Text Solution

    |

  10. int(0)^(100pi)(|sin^(3)x|+|cos^(3)x|)dx=

    Text Solution

    |

  11. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

    Text Solution

    |

  12. overset(2pi) underset(0)int(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0...

    Text Solution

    |

  13. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

    Text Solution

    |

  14. int(0)^(sqrt("log"(pi)/2))cos(e^(x^(2)))2xe^(x^(2))dx=

    Text Solution

    |

  15. If f(x)=int(0)^(x)sin^(6)tdt, then f(x+pi)=

    Text Solution

    |

  16. If f(x) is a polynomial of degree 2, such that f(0)=3,f'(0)=-7,f''(0)=...

    Text Solution

    |

  17. If f(x)=Asin((pix)/2)+B, f'(1/2)=sqrt2 and int0^1 f(x)dx=(2A)/pi then ...

    Text Solution

    |

  18. If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

    Text Solution

    |

  19. If a is a positive integer, then the number of values of a satisfying ...

    Text Solution

    |

  20. If for all real numbers y ,[y] is the greatest integer less than or eq...

    Text Solution

    |