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

Let `f : [-1,2]rarr[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) x f(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) = 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|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - IV|9 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

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

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:[-2,3]rarr[0,oo) be a continuous function such that f(1-x)=f(x) for all x in[-2,3]. If R_(1) is the numerical value of the area of the region bounded by y=f(x),x-2,x=3 and the axis of x and R_(2)=int_(-2)^(3)xf(x)dx, then

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these

let f:R rarr R be a continuous function defined by f(x)=(1)/(e^(x)+2e^(-x))

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"

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

A continous function f(x) is such that f(3x)=2f(x), AA x in R . If int_(0)^(1)f(x)dx=1, then int_(1)^(3)f(x)dx is equal to

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. The value of int(sqrt(ln2))^(ln3)(xsinx^(2))/(sinx^(2)+sin(ln6-x^(2)))...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  5. The value of the integral int(-pi//2)^(pi//2) (x^(2)+ln'(pi+x)/(x-a)) ...

    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 curvesy= sinx+cosx and y = | cosx-sin x | ove...

    Text Solution

    |

  10. Let f : [1/2, 1] rarr R (the set of the all real numbers) be a positiv...

    Text Solution

    |

  11. For a in R (the set of all real numbers), a ne = - 1, lim(nrarroo)((...

    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) rArr R be given f(x) = underset(1/x)overset(x)e^((1+(dt...

    Text Solution

    |

  14. The value of int(0)^(1) 4x^(3){(d^(2))/(dx^(2))(1-x^(2))^(5)}dx is

    Text Solution

    |

  15. The following integral int(pi/4)^(pi/2)(2cosecx)^(17) dx is equal to

    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. Text Solution

    |

  19. Let f : R rarr R be a function defined by f(x) ={{:([x],xle2),(0,xgt...

    Text Solution

    |

  20. If alpha = int(0)^(1)e^(9x+3tan^(-1)x)) ((12+9x^(2))/(1+x^(2)))dx wher...

    Text Solution

    |