Home
Class 12
MATHS
The function f and g are positive and co...

The function `f` and `g` are positive and continuous. If `f` is increasing and `g` is decreasing, then `int_0^1f(x)[g(x)-g(1-x)]dx`
(a)is always non-positive
(b)is always non-negative
(c)can take positive and negative values
(d)none of these

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

int [f(x)g"(x) - f"(x)g(x)]dx is

Evaluate: int[f(x)g''(x)-f ''(x)g(x)]dx

Let f and g be increasing and decreasing functions, respectively, from [0,oo]to[0,oo]dot Let h(x)=f(g(x))dot If h(0)=0, then h(x)-h(1) is (a)always zero (b) always negative always positive (d) strictly increasing none of these

Which of the following statement is always true? (a)If f(x) is increasing, the f^(-1)(x) is decreasing. (b)If f(x) is increasing, then 1/(f(x)) is also increasing. (c)If fa n dg are positive functions and f is increasing and g is decreasing, then f/g is a decreasing function. (d)If fa n dg are positive functions and f is decreasing and g is increasing, the f/g is a decreasing function.

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

Let f: R to R and g: R to R be continuous function. Then the value of the integral int_(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)-g(-x)]dxi s (a) pi (b) 1 (c) -1 (d) 0

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these

If f(x)a n dg(x) are continuous functions, then int_(1nlambda)^(1n1/lambda)(f((x^2)/4)[f(x)-f(-x)])/(g((x^2)/4)[g(x)+g(-x)])dx is (a)dependent on lambda (b) a none-zero constant (c)zero (d) none of these

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? (a) [f(x)]^(g(x)) is always increasing (b) [f(x)]^(g(x)) is decreasing, when f(x) 1,t h e n[f(x)]^(g(x)) is increasing.

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. about to only mathematics

    Text Solution

    |

  2. If f(x)={0 ,where x=n/(n+1),n=1,2,3.... and 1 else where then the va...

    Text Solution

    |

  3. The function f and g are positive and continuous. If f is increasing a...

    Text Solution

    |

  4. A Function f(x) satisfies the relation f(x)=e^x+int0^1e^xf(t)dtdot T...

    Text Solution

    |

  5. Let f(x) be positive, continuous, and differentiable on the interval ...

    Text Solution

    |

  6. Letf: (0,oo)->R andF(x^3)=int0^ (x^3)f(t)dt, if F(x^3)=x^3(x^2+x+1).Th...

    Text Solution

    |

  7. Ifg(x)=int0^x2|t|dt,then (a)g(x)=x|x| (b)g(x) is monotonic (c) g(x...

    Text Solution

    |

  8. Prove that the value of the integral, int(0)^(2a)(f(x))/(f(x)+f(2a-x)...

    Text Solution

    |

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

    Text Solution

    |

  10. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  11. int(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

    Text Solution

    |

  12. The value of int(in2)^sqrt(in3) (xsinx^2)/(sinx^2+sin(In6-x^2)dx is

    Text Solution

    |

  13. Let f be a non-negative function defined on the interval [0,1]. If int...

    Text Solution

    |

  14. (lim)(n to oo)n/(2^n)int0^2x^n dx equals

    Text Solution

    |

  15. Let f:[0,oo) to R be a continuous strictly increasing function, such t...

    Text Solution

    |

  16. A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint0^...

    Text Solution

    |

  17. L e tf(x)=x^3-(3x^2)/2+x+1/4 Then the value of (int(1/4)^(3/4)f(f(x...

    Text Solution

    |

  18. Evaluate: int0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest inte...

    Text Solution

    |

  19. Consider the polynomial f(x)=a x^2+b x+c dot If f(0)=0,f(2)=2, then th...

    Text Solution

    |

  20. Find the points at which the function f given by f(x)=x^3-3x has local...

    Text Solution

    |