Home
Class 12
MATHS
Let int(0)^(a)f(x)dx = lambda and int(0)...

Let `int_(0)^(a)f(x)dx = lambda` and `int_(0)^(a)f(2a-x)dx=mu`. Then `int_(0)^(2a)f(x)dx` is :

A

`lambda+mu`

B

`lambda-mu`

C

`2 lambda-mu`

D

`lambda-2mu`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test 2|56 Videos

  • DEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|143 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 Videos

  • DERIVATIVE AS A RATE MEASURER

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|26 Videos

Similar Questions

Explore conceptually related problems

int_(m)^(0)f(x)dx is

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

Prove that int_(0)^(a)f(x)g(a-x)dx=int_(0)^(a)g(x)f(a-x)dx .

If int_0^af(2a-x)dx=m and int_0^af(x)dx=n, then int_0^(2a) f(x) dx is equal to

Prove that int_(a)^(b)f(x)dx=(b-a)int_(0)^(1)f((b-a)x+a)dx

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

Prove that: int_0^(2a)f(x)dx=int_0^(2a)f(2a-x)dxdot

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nT+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

int_n^(n+1)f(x) dx=n^2+n then int_(-1)^1 f(x) dx =

Let int_(a)^(b)f(x)dx=int_(a+c)^(b+c)f(x-c)dx . Then the value of int_(0)^(pi)sin^(2010)x*cos^(2009)xdx is

OBJECTIVE RD SHARMA ENGLISH-DEFINITE INTEGRALS-Chapter Test 1
  1. The smallest interval [a,b] such that int0^(1) (1)/(sqrt(1+x^(4)))dx...

    Text Solution

    |

  2. Let I(n)=int(0)^(pi//2) sin^(n)x dx, nin N. Then

    Text Solution

    |

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

    Text Solution

    |

  4. int(0)^(pi)(dx)/(1+3^(cos x)) is equal to:

    Text Solution

    |

  5. Let int(0)^(a)f(x)dx = lambda and int(0)^(a)f(2a-x)dx=mu. Then int(0)^...

    Text Solution

    |

  6. Evaluate : int((pi)/(4))^((3pi)/(4))(x)/(1+sinx)dx

    Text Solution

    |

  7. Let I(n)=int(0)^(pi//2) cos^(n)x cos nx dx. Then, I(n):I(n+1) is equal...

    Text Solution

    |

  8. The value of int(-1)^(1) max[2-x,2,1+x] dx is

    Text Solution

    |

  9. int(0)^(pi//4) sin(x-[x]) dx is equalto

    Text Solution

    |

  10. The value of the integral int(-1)^(1) (x-[2x])dx,is

    Text Solution

    |

  11. Let f:R in R be a continuous function such that f(1)=2. If lim(x to 1)...

    Text Solution

    |

  12. Let f:R in R be a continuous function such that f(x) is not identicall...

    Text Solution

    |

  13. Let f(x)=int(0)^(x) |xx-2|dx, ge 0. Then, f'(x) is

    Text Solution

    |

  14. Lt(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0, is equal to (A) k/e (B) e/k (C)...

    Text Solution

    |

  15. int(0)^(sqrt(2)) [x^(2)]dx, is

    Text Solution

    |

  16. Let f(x) be a function satisfying f'(x)=f(x), f(0)=1 and g be a functi...

    Text Solution

    |

  17. (sum(n=1)^10int(-2n-1)^(-2n)sin^(27)(x)dx+sum(n=1)^10int(2n)^(2n+1)sin...

    Text Solution

    |

  18. If f(y)=e^(y),g(y)=y,ygt0 and F(t)=int(0)^(1)f(t-y)g(y)dt then

    Text Solution

    |

  19. If I(n)=int(0)^(pi//2) x^(n) sin x dx, then I(4)+12I(2) is equal to\

    Text Solution

    |

  20. int(0)^(1) sin{2 tan^(-1)sqrt((1+x)/(1-x))}dx=

    Text Solution

    |