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

  • APPICATIONS OF DEFINITE INTEGRAL

    TARGET PUBLICATION|Exercise EVALUATION TEST|18 Videos
  • APPICATIONS OF DEFINITE INTEGRAL

    TARGET PUBLICATION|Exercise CRITICAL THINKING|48 Videos
  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 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]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: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: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 rarr R be a continuous function defined by f(x)=(1)/(e^(x)+2e^(-x))

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

Let f: [1,3] to R be a continuous function that is differentiable in (1,3) and f '(x) = |f(x) |^(2) + 4 for all x in (1,3). Then,

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:R rarr R be a differentiable and strictly decreasing function such that f(0)=1 and f(1)=0. For x in R, let F(x)=int_(0)^(x)(t-2)f(t)dt

TARGET PUBLICATION-APPICATIONS OF DEFINITE INTEGRAL-COMPETITIVE THINKING
  1. Find the area bounded by the x-axis, part of the curve y=(1-8/(x^2)) ,...

    Text Solution

    |

  2. If a curve y = asqrt(x)+bx passes through the point (1,2) and the area...

    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. Area of the region bounded by y=cosx,x=0,x=pi and X-axis is . . .sq....

    Text Solution

    |

  5. The area bounded by the curve y = sin^(2) x, 0 le x le pi/2, X axis an...

    Text Solution

    |

  6. the area included between the curve xy^(2)=a^(2)(a-x) and y -axis is ...

    Text Solution

    |

  7. The area of the region bounded by x^(2)=4y,y=1,y=4 and the Y-axis lyin...

    Text Solution

    |

  8. Find the area enclosed by the curves x^2=y , y=x+2, and x axis

    Text Solution

    |

  9. The area (in sqaure units) of the region enclosed by the curves y=x,x=...

    Text Solution

    |

  10. Area bounded between two latus-rectum of the ellipse x^(2)/a^(2)+y^(2)...

    Text Solution

    |

  11. The area formed by triangular shaped region bounded by the curves y=si...

    Text Solution

    |

  12. Find the area of the region included between the parabolas y^2=4a x...

    Text Solution

    |

  13. The area of the region bounded by the curves y=x^(2) " and " x=y^(2) i...

    Text Solution

    |

  14. Find the area of the figure bounded by the parabolas x=-2y^2, x=1-3y^2...

    Text Solution

    |

  15. What is the area bounded by the curve y = x^(2) and the line y = 16 ...

    Text Solution

    |

  16. Find the area bounded by the parabola y^2 = 4ax and the line y = 2ax.

    Text Solution

    |

  17. Area lying between the curves y^(2)=2x and y=x is

    Text Solution

    |

  18. The area of the region bounded by the curves x=y^(2)-2 and x=y is

    Text Solution

    |

  19. If the area enclosed between the curves y=a x^2a n dx=a y^2(a >0) is 1...

    Text Solution

    |

  20. Find the ratio in which the area bounded by the curves y^2=12 xa n dx^...

    Text Solution

    |