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

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|20 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 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

ARIHANT MATHS-AREA OF BOUNDED REGIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let C1 and C2, be the graph of the functions y= x^2 and y= 2x, 0<=x<=...

    Text Solution

    |

  2. Area of region {(x,y) in R^(2): y ge sqrt(|x+3|,)5y le x + 9 le 15}

    Text Solution

    |

  3. Let F(x)=intx^[x^2+pi/6][2cos^2t.dt] for all x in R and f:[0,1/2] -> [...

    Text Solution

    |

  4. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

    Text Solution

    |

  5. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Area of the region bounded by the curve y=e^(x) and linesx=0 and y=e i...

    Text Solution

    |

  10. The area of the region bounded by the curves y=sqrt[[1+sinx]/cosx] and...

    Text Solution

    |

  11. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  12. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  13. Consider the function defined implicitly by the equation y^3-3y+x=0 on...

    Text Solution

    |

  14. The area (in sqaure units) of the region {(x,y):x ge 0, x + y le 3, x^...

    Text Solution

    |

  15. The area (in sq units) of the region {(x, y) : y^2 gt= 2x and x^2 + y^...

    Text Solution

    |

  16. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

    Text Solution

    |

  17. The area (in sq. units) of the quadrilateral formed by the tangents...

    Text Solution

    |

  18. The area of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^...

    Text Solution

    |

  19. The area (in square units) bounded by the curves y=sqrt(x),2y-x+3=0, x...

    Text Solution

    |

  20. The area bounded between the parabola x^(2)=y/4 and x^(2)=9y and the s...

    Text Solution

    |

  21. The area of the region enclosed by the curves y=x, x=e,y=(1)/(x) and t...

    Text Solution

    |