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

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`

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=1/(k+1)[x^4-kx^3+(2k-4)x^2]`
Promotional Banner

Topper's Solved these Questions

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Area of bounded Regions Exercise 7: Subjective Type Questions|1 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Integer Answer Type Questions)|8 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 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-a xi s , and line x=t(w h e r e0lt=tlt=2)dot

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 .

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

The area bounded by y = tan x, y = cot x, X-axis in 0 lt=x lt= pi/2 is

The area bounded by the parabola y=4x^(2),y=(x^(2))/(9) and the line y = 2 is

Let f(x)= minimum {e^(x),3//2,1+e^(-x)},0lexle1 . Find the area bounded by y=f(x) , X-axis and the line x=1.

The area bounded by the curve y^(2) = 4x and the line 2x-3y+4=0 is

Find the area bounded by the curve y=sin^(-1)x and the line x=0,|y|=pi/2dot

Find the area bounded by the curve y=sin^(-1)x and the line x=0,|y|=pi/2dot

ARIHANT MATHS ENGLISH-AREA OF BOUNDED REGIONS-Exercise (Subjective Type Questions)
  1. Find the continuous function f where (x^4-4x^2)lt=f(x)lt=(2x^2-x^3) su...

    Text Solution

    |

  2. Let f(t)=|t-1|-|t|+|t+1|, AA t in R. Find g(x) = max {f(t):x+1letlex+2...

    Text Solution

    |

  3. Let f(x)= minimum {e^(x),3//2,1+e^(-x)},0lexle1. Find the area bounded...

    Text Solution

    |

  4. Find the area bounded by y=f(x) and the curve y=2/(1+x^2) satisfying ...

    Text Solution

    |

  5. The value of overset(sin^(2)x)underset(0)int sin^(-1)sqrt(t)dt+overs...

    Text Solution

    |

  6. Let T be an acute triangle Inscribe a pair R,S of rectangle in T as sh...

    Text Solution

    |

  7. Find the maximum area of the ellipse that can be inscribed in an isoce...

    Text Solution

    |

  8. Find the area of the region bounded by curve y=25^(x)+16 and the curve...

    Text Solution

    |

  9. If the circles of the maximum area inscriabed in the region bounded by...

    Text Solution

    |

  10. Find limit of the ratio of the area of the triangle formed by the orig...

    Text Solution

    |

  11. Find the area of curve enclosed by |x+y|+|x-y|le4,|x|le1, y ge sqrt(x^...

    Text Solution

    |

  12. Calculate the area enclosed by the curve 4lex^(2)+y^(2)le2(|x|+|y|).

    Text Solution

    |

  13. Find the area enclosed by the curve [x]+[y]-4 in 1st quadrant (where [...

    Text Solution

    |

  14. Sketch the region and find the area bounded by the curves |y+x|le1,|y-...

    Text Solution

    |

  15. Find the area of the region bounded by the curve 2^(|x|)|y|+2^(|x|-1)l...

    Text Solution

    |

  16. The value of the parameter a(a>=1) for which the area of the figure bo...

    Text Solution

    |