Home
Class 12
MATHS
Let f:[-1,2]vec[0,oo) be a continuous fu...

Let `f:[-1,2]vec[0,oo)` be a continuous function such that `f(x)=f(1-x)fora l lx in [-1,2]dot` Let `R_1=int_(-1)^2xf(x)dx ,` and `R_2` be the area of the region bounded by `y=f(x),x=-1,x=2,` and the `x-a xi s` . Then `R_1=2R_2` (b) `R_1=3R_2` `2R_1` (d) `3R_1=R_2`

A

`R_(1) = 2R_(2)`

B

`R_(1) = 3R_(2)`

C

`2R_(1) = R_(2)`

D

`3R_(1) = R_(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 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

Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fora l lx in [-1,2]dot Let R_1=int_(-1)^2xf(x)dx , and R_2 be the area of the region bounded by y=f(x),x=-1,x=2, and the x-axis . Then (a) R_1=2R_2 (b) R_1=3R_2 (c) 2R_1 (d) 3R_1=R_2

Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fora l lx in [-1,2]dot Let R_1=int_(-1)^2xf(x)dx , and R_2 be the area of the region bounded by y=f(x),x=-1,x=2, and the x- axis . Then R_1=2R_2 (b) R_1=3R_2 (c) 2R_1=R_2 (d) 3R_1=R_2

Let f:[1,2] to [0,oo) be a continuous function such that f(x)=f(1-x) for all x in [-1,2]. Let R_(1)=int_(-1)^(2) xf(x) dx, and R_(2) be the area of the region bounded by y=f(x),x=-1,x=2 and the x-axis . Then,

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:R in R be a continuous function such that f(1)=2. If lim_(x to 1) int_(2)^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R . If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to

Let f(x) be a function defined on R satisfyin f(x) =f(1-x) for all x in R . Then int_(-1//2)^(1//2) f(x+(1)/(2))sin x dx equals

Let f be a real vlaued fuction with domain R such that f(x+1)+f(x-1)=sqrt(2)f(x) for all x in R , then ,

If f: R->R is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

If f:R->R is a twice differentiable function such that f''(x) > 0 for all x in R, and f(1/2)=1/2 and f(1)=1, then

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. T h ev a l u eofint(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^...

    Text Solution

    |

  2. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

    Text Solution

    |

  3. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  4. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  5. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  6. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  7. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  8. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

    Text Solution

    |

  9. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

    Text Solution

    |

  10. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  11. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  12. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  13. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  14. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  15. The following integral int(pi//4)^(pi//2)(2cosec x)^(17) dx dx is equa...

    Text Solution

    |

  16. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  17. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |

  18. ((int(-1/2)^(1/2)cos 2x *log((1+x)/(1-x))dx))/((int(0)^(1/2)cos 2x *lo...

    Text Solution

    |

  19. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

    Text Solution

    |

  20. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

    Text Solution

    |