Home
Class 12
MATHS
Let C1C2 be the graphs of the functions ...

Let `C_1C_2` be the graphs of the functions `y=x^2` and `y=2x ,` respectively, where `0lt=xlt=1.` Let `C_3` be the graph of a function `y=f(x),` where `0lt=xlt=1, f(0) =0.` For a point `P` on `C_1,` let the lines through `P ,` parallel to the axis, meet `C_2` and `C_3` at `Q` and `R ,` respectively (see Figure). If for every position of `P(onC_1),` the areas of the shaded regions `OPQ` and `ORP` are equal, determine the function `f(x)`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise All Questions|674 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise Subjective Type|2 Videos

Similar Questions

Explore conceptually related problems

Find the maxima and minima of the function y=x(x-1)^2,0lt=xlt=2.

Consider the function f(x)={2x+3, x le 1 and -x^2+6, x > 1 Then draw the graph of the function y=f(x), y=f(|x|) and y=|f(x)|.

Let C_(1) and C_(2) denote the centres of the circles x^(2) +y^(2) = 4 and (x -2)^(2) + y^(2) = 1 respectively and let P and Q be their points of intersection. Then the areas of triangles C_(1) PQ and C_(2) PQ are in the ratio _

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

Let f:[0,1] rarr [0,1] be a continuous function. Then prove that f(x)=x for at least one 0lt=xlt=1.

If the area of the region {(x , y):0lt=ylt=x^2+1,0lt=ylt=x+1,0lt=xlt=2} is A , then the value of 3A-17 is____

Two circles C_1 and C_2 intersect at two distinct points P and Q in a line passing through P meets circles C_1 and C_2 at A and B , respectively. Let Y be the midpoint of A B and Q Y meets circles C_1 and C_2 at X a n d Z respectively. Then prove that Y is the midpoint of X Z

Let a function f(x) be defined by f(x)=x^(3)-2x in [0, sqrt(2)] , then the value of c in Rolle's theorem is -

A line through point A(1,3) and parallel to the line x-y+1 = 0 meets the line 2x-3y + 9 = 0 at point P. Find distance AP without finding point P.

Let f(x) =M a xi mu m {x^2,(1-x)^2,2x(1-x)}, where 0lt=xlt=1. Determine the area of the region bounded by the curves y=f(x) ,x-axis ,x=0, and x=1.

CENGAGE PUBLICATION-APPLICATION OF INTEGRALS-All Questions
  1. Let C be a curve passing through M(2,2) such that the slope of the tan...

    Text Solution

    |

  2. Let f(x) be continuous function given by f(x)={2x ,|x|lt=1and x^2+a x+...

    Text Solution

    |

  3. Let C1C2 be the graphs of the functions y=x^2 and y=2x , respectively,...

    Text Solution

    |

  4. Find the area bounded by the curve x^(2) = 4y and the line x = 4y - 2.

    Text Solution

    |

  5. The area of the region bounded by the curves y=x^(2),y=|2-x^(2)| and y...

    Text Solution

    |

  6. If [(4a^2,4a, 1),(4b^2, 4b,1), (4c^2, 4c, 1)] [(f(-1)),(f(1)),(f(2))] ...

    Text Solution

    |

  7. If f(x) is a function such that f'(x)=(x-1)^2 (4-x), then

    Text Solution

    |

  8. The area bounded by the curves y=|x|-1a n dy=-|x|+1 is 1 sq. units (b)...

    Text Solution

    |

  9. If the area bounded by the curve y=f(x), x-axis and the ordinates x=1 ...

    Text Solution

    |

  10. The area bounded by the parabolas y=(x+1)^2 and y=(x-1)^2a n dy=(x-1)^...

    Text Solution

    |

  11. The area bounded by the curves y=sqrt(x),2y+3=x , and x-axis in the 1s...

    Text Solution

    |

  12. Find the area bounded by y=tan^(-1)x , y=cot^(-1)x ,and y-axis in the...

    Text Solution

    |

  13. the equation to the director circle of (x^2)/6+(y^2)/4=1 is

    Text Solution

    |

  14. Find the area bounded by y=loge x , y=-loge x ,y=loge(-x),a n dy=-loge...

    Text Solution

    |

  15. The area of region for which 0 lt y lt 3 - 2x-x^2 and x gt 0 is

    Text Solution

    |

  16. The area common to regions x^2+y^2-2xlt=0 and ygeq sin (pix/2)

    Text Solution

    |

  17. Draw the rough sketch of the curve y=x^(4)-x^(2).

    Text Solution

    |

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

    Text Solution

    |

  19. Find the continuous function f where (x^4-4x^2)lt=f(x)lt=(2x^2-x^3) su...

    Text Solution

    |

  20. Find the area bounded by the curves y=-x^2+6x-5,y=-x^2+4x-3, and the s...

    Text Solution

    |