Home
Class 12
MATHS
Let C1 and C2, be the graph of the func...

Let `C_1 and C_2`, be the graph of the functions `y= x^2 and y= 2x, 0<=x<= 1` respectively. Let `C_3`, be the graph of a function `y- (fx), 0<=x<=1, f(0)=0`. For a point Pand `C_2`, let the lines through P, parallel to the axes, meet `C_2 and C_3`, at Q and R respectively. If for every position of P (on `C_1`), the areas of the shaded regions `OPQ and ORP` are equal, determine the function `f(x)`.

Text Solution

Verified by Experts

The correct Answer is:
`f(x) = x^(3) - x^(2)`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 3 Part - II|25 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

Sketch the graph of the function y=2|x-2|-|x+1|+x.

If the graph of the function y=(a-b)^(2)x^(2)+2(a+b-2c)x+1(AA a ne b)

Draw the graphs of the functions y^(2)=x+1 and y^(2)=-x+1 and also find the area bounded by these curves.

Let C_(1) and C_(2) be two circles whose equations are x^(2)+y^(2)-2x=0 and x^(2)+y^(2)+2x=0 and P(lambda,lambda) is a variable point

Let C_(1) be the graph of xy=1 and the reflection of C_(1) in the line y=2x is C_(2) . If the equation of C_(2) is expressed as 12x^(2)+bxy+cy^(2)+d=0 , then the value of (b+c+d) is equal to

Let f(x)=x^(2)+bx+c AA x in R,(b,c in R) attains its least value at x=-1 and the graph of f(x) cuts y-axis at y=2

Let C_(1) and C_(2) be the circles x^(2) + y^(2) - 2x - 2y - 2 = 0 and x^(2) + y^(2) - 6x - 6y + 14 = 0 respectively. If P and Q are points of intersection of these circles, then the area (in sq. units ) of the quadrilateral PC_(1) QC_(2) is :

If the graph of the function y = f(x) is as shown : The graph of y = 1//2(|f(x)|-f(x)) is

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -High Level Problem
  1. Given that lim(x to oo)(int(0)^(x)(t^(2))/(sqrt(a+t))dt)/(bx-sinx) = 1...

    Text Solution

    |

  2. Draw a graph of the function f(x) = cos^(-1) (4x^(3)-3x), x in [-1,1] ...

    Text Solution

    |

  3. Consider a square with vertices at (1,1),(-1,1),(-1,-1),a n d(1,-1)dot...

    Text Solution

    |

  4. If [x] denotes the greatest integer function. Draw a rough sketch of t...

    Text Solution

    |

  5. Find the area of the region bounded by y = f(x), y = |g(x)| and the li...

    Text Solution

    |

  6. Let f(x)={{:(-2",",-3lexle0),(x-2",",0ltxle3):}andg(x)=f(|x|)+|f(x)| ...

    Text Solution

    |

  7. Find the area of region {(x,y):0leylex^(2)+1, 0 le y le x+ 1, 0 le x ...

    Text Solution

    |

  8. A curve y=f(x) passes through point P(1,1) . The normal to the curv...

    Text Solution

    |

  9. Find the area bounded by y = [-0. 01 x^(4) - 0.02 x^(2)], (where [*] ...

    Text Solution

    |

  10. Let ABC be a triangle with vertices A -=(6,,2sqrt3+1))),B-=(4,2)and C-...

    Text Solution

    |

  11. Find the area of the region which is inside the parabola satisfying t...

    Text Solution

    |

  12. Find the area of the region which is inside the parabola y = - x^(2) +...

    Text Solution

    |

  13. Consider the curve C: y = sin 2x - sqrt(3)|sinx|, C cuts the x-axis at...

    Text Solution

    |

  14. Area bounded by the line y=x, curve y=f(x),(f(x)gtx,AA xgt1) and the l...

    Text Solution

    |

  15. Consider the two curves y = 1//x^(2) and y = 1//[4(x-1)]. At what v...

    Text Solution

    |

  16. Let C1 and C2, be the graph of the functions y= x^2 and y= 2x, 0<=x<=...

    Text Solution

    |

  17. Given the parabola C : y = x^(2). If the circle at y axis with radius...

    Text Solution

    |

  18. If [(4a^2,4a,1),(4b^2,4b,1),(4c^2,4c,1)][(f(-1)),(f(1)),(f(2))][(3a^2...

    Text Solution

    |

  19. f(x) and g(x) are polynomical of degree 2 such that |int(a(1))^(a(2...

    Text Solution

    |

  20. Let L = 4x- 5y, L(i) = (x)/(10) - (i)/(n), L(i) = x/10 + y/8 + i/n, a...

    Text Solution

    |