Home
Class 12
MATHS
Let f: Rveca n dg: RvecR be continuous f...

Let `f: Rveca n dg: RvecR` 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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

If f(x)=(2-xcosx)/(2+xcosx)andg(x)= "log"_(e)x, (xgt0) then the value of the integral int_(-pi//4)^(pi//4)g(f(x)) dx is

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

If f(x) and g(x) are continuous functions, then int_(In lamda)^(In (1//lamda))(f(x^(2)//4)[f(x)-f(-x)])/(g(x^(2)//4)[g(x)+g(-x)])dx is

Let f:[0,1]to R be a continuous function then the maximum value of int_(0)^(1)f(x).x^(2)dx-int_(0)^(1)x.(f(x))^(2)dx for all such function(s) is:

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)])dxi s (a)dependent on lambda (b) a none-zero constant (c)zero (d) none of these

Let f: RvecR and g: Rvec be two functions such that fog(x)=sinx^2a n d gof(x)= sin^2x dot Then, find f(x)a n dg(x)dot

If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi-x) =1=g (x)+g(pi-x) then int_(0)^(pi) [f(x)+g(x)] dx is equal to

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

Let f: Rveca n dg: RvecR be defined by f(x)=x+1a n dg(x)=x-1. Show that fog=gof=I_Rdot

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Let f(x) be an odd continous function which is periodic with period 2....

    Text Solution

    |

  2. Evaluate inta^b(dx)/(sqrt(x)),w h e r ea , b > 0.

    Text Solution

    |

  3. Let f: Rveca n dg: RvecR be continuous function. Then the value of the...

    Text Solution

    |

  4. Evaluate: int(-(3pi)/2)^(-pi/2)[(x+pi)^3+cos^2(x+3pi)]dx

    Text Solution

    |

  5. Evaluate: int0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx

    Text Solution

    |

  6. Evaluate: int0^(100)x-[x]dx where [dot] represents the greatest in...

    Text Solution

    |

  7. If Sn=[1/(1+sqrt(n))+1/(2+sqrt(2n))+....+1/(n+sqrt(n^2))] then (lim)(n...

    Text Solution

    |

  8. The value of ("lim")(nvecoo)sum(r=1)^(4n)(sqrt(n))/(sqrt(r)(3sqrt(r)+s...

    Text Solution

    |

  9. Evaluate: (int0n[x]dx)/(int0n{x}dx)(w h e r e[x]a n d{x} are integral...

    Text Solution

    |

  10. Evaluate: int(-pi/4)^(npi-pi/4)|sinx+cosx|dx

    Text Solution

    |

  11. The value of int0^(pi/2) (dx)/(1+tan^3 x) is (a) 0 (b) 1 (c) pi/2 (d) ...

    Text Solution

    |

  12. Evaluate: int(-pi)^pi(1-x^2)sinxcos^2xdx

    Text Solution

    |

  13. Let f be a contiuous function on [a,b]. If F(x)=(int(a)^(x)f(t)dt-int(...

    Text Solution

    |

  14. Evaluate the following: int(-1)^(1)(sin x-x^(2))/(3-|x|)dx

    Text Solution

    |

  15. If int(a)^(b)|sinx|dx=8 and int(0)^(a+b)|cosx|dx=9, then

    Text Solution

    |

  16. Evaluate: int(-pi/2)^(pi/2)sqrt(cos^(2n-1)x-cos^(2n+1)x)dx ,w h e r en...

    Text Solution

    |

  17. f(x) is a continuous and bijective function on Rdot If AAt in R , the...

    Text Solution

    |

  18. Evaluate: int(-1/2)^(1/2)cosxlog((1-x)/(1+x))dx

    Text Solution

    |

  19. f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

    Text Solution

    |

  20. Evaluate: int0^x[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[do...

    Text Solution

    |