Home
Class 12
MATHS
Find a continuous function f, where (x^(...

Find a continuous function f, where `(x^(4)-4x^(2))lef (x) le (2x^(2)-x^(3))` such that the area bounded by `y=f(x), y=x^(4)-4x^(2),` the y-axis, and the line `x=t," where "(0letle2)` is k times the area bounded by `y=f(x),y=2x^(2)-x^(3),` y-axis, and line `x=t("where "0le t le 2).`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE ENGLISH|Exercise MATRIX MATCH TYPE|3 Videos
  • APPLICATIONS OF DERIVATIVES

    CENGAGE ENGLISH|Exercise Comprehension Type|5 Videos

Similar Questions

Explore conceptually related problems

Find the continuous function f where (x^4-4x^2)lt=f(x)lt=(2x^2-x^3) such that the area bounded by y=f(x),y=x^4-4x^2dot then y-axis, and the line x=t , where (0lt=tlt=2) is k times the area bounded by y=f(x),y=2x^2-x^3 ,y-axis , and line x=t(w h e r e0lt=tlt=2)dot

Find the continuous function f where (x^4-4x^2)lt=f(x)lt=(2x^2-x^3) such that the area bounded by y=f(x),y=x^4-4x^2dot then y-axis, and the line x=t , where (0lt=tlt=2) is k times the area bounded by y=f(x),y=2x^2-x^3,y-a xi s , and line x=t(w h e r e0lt=tlt=2)dot

Find the area bounded by the parabola y=x^(2), the x -axis and the lines x=-1, x=2 .

The area bounded by the curve y=4x-x^2 and the x -axis is:

Find the area bounded by the curve y=4x-x^2 , the x-axis and the ordinates x=1 and x=3 .

The area bounded by y=4-x^(2),y=0 and y = 3 is

The area bounded by y = f(x), x-axis and the line y = 1, where f(x)=1+1/x int_1^xf(t)dt is

Find the area bounded by y=-x^(3)+x^(2)+16x and y=4x

Find the area of the region bounded by x^(2)=8y , x-axis and the line x= 4

The area bounded by the curve y=4-x^(2) and X-axis is

CENGAGE ENGLISH-APPLICATION OF INTEGRALS-All Questions
  1. Let A(k) be the area bounded by the curves y=x^2-3 and y=k x+2 The ra...

    Text Solution

    |

  2. int (ax^2+bx+c)dx =

    Text Solution

    |

  3. Find a continuous function f, where (x^(4)-4x^(2))lef (x) le (2x^(2)-x...

    Text Solution

    |

  4. The parabolas y^2=4xa n dx^2=4y divide the square region bounded by th...

    Text Solution

    |

  5. Statement 1 : The area bounded by parabola y=x^2-4x+3a n dy=0 is 4/3 s...

    Text Solution

    |

  6. f(x) is a polynomial of degree 3 passing through the origin having loc...

    Text Solution

    |

  7. int x^2(1-1/x^2)dx =

    Text Solution

    |

  8. The value of a(a >0) for which the area bounded by the curves y=x/6+1/...

    Text Solution

    |

  9. Area bounded by the relation [2x]+[y]=5, x , y >0 is

    Text Solution

    |

  10. The area bounded by the curves y=x(x-3)^2a n dy=x is (in sq. units)

    Text Solution

    |

  11. If the area of the region {(x , y):0lt=ylt=x^2+1,0lt=ylt=x+1,0lt=xlt=2...

    Text Solution

    |

  12. The area enclosed by f(x)=12+a x-x^2 coordinates axes and the ordinat...

    Text Solution

    |

  13. If the area bounded by the curve f(x)=x^(1/3)(x-1) and the x-axis is A...

    Text Solution

    |

  14. If the area bounded by the curve y=x^2+1 and the tangents to it drawn ...

    Text Solution

    |

  15. If the area enclosed by the curve y=sqrt(x) and x=-sqrt(y) , the circl...

    Text Solution

    |

  16. Which of the following abnormalities is due to X-linked recessive ...

    Text Solution

    |

  17. If A is the area bounded by the curves y=sqrt(1-x^2) and y=x^3-x , the...

    Text Solution

    |

  18. A curve is given by y={(sqrt(4-x^2)),0lt=x<1and sqrt((3x)),1lt=xlt=...

    Text Solution

    |

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

    Text Solution

    |

  20. Find the area of the region bounded by the curves y=x^2+2, y=x ,x=0,a ...

    Text Solution

    |