Home
Class 12
MATHS
Suppose y=f(x) and y=g(x) are two contin...

Suppose `y=f(x)` and `y=g(x)` are two continuous functiond whose graphs intersect at the three points `(0,4),(2,2)` and `(4,0)` with `f(x) gt g(x)` for ` 0 lt x lt 2` and `f(x) lt g(x)` for `2 lt x lt 4`. If `int_0^4[f(x)-g(x)]dx=10 and int_2^4[g(x)-f(x)]dx=5` the area between two curves for `0 lt x lt 2`,is (A) 5 (B) 10 (C) 15 (D) 20

A

5

B

10

C

15

D

20

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • AREA UNDER THE CURVE

    MOTION|Exercise EXERCISE - 2 (LEVEL-II)|4 Videos

  • AREA UNDER THE CURVE

    MOTION|Exercise EXERCISE -3|34 Videos

  • AREA UNDER THE CURVE

    MOTION|Exercise EXERCISE - 1|17 Videos

  • BASIC MATHEMATIC & LOGARITHM

    MOTION|Exercise Exercise - 4|4 Videos

Similar Questions

Explore conceptually related problems

If f(x)=sqrt(x-2) , for 2 lt x lt 4 , then f(x) is

If f(x)=f(4-x), g(x)+g(4-x)=3 and int_(0)^(4)f(x)dx=2 , then : int_(0)^(4)f(x)g(x)dx=

If f(x) and g(x) be continuous functions in [0,a] such that f(x)=f(a-x),g(x)+g(a-x)=2 and int_0^a f(x)dx=k , then int_0^a f(x)g(x)dx= (A) 0 (B) k (C) 2k (D) none of these

f(x) and g(x) are differentiable functions for 0 le x le 2 such that f(0)=5, g(0)=0, f(2)=8, g(2)=1 . Show that there exists a number c satisfying 0 lt c lt 2 and f'(c)=3g'(c) .

If f and g are continuous functions on [0,a] such that f(x)=f(a-x) and g(x)+g(a-x)=2 then show that int_(0)^(a)f(x)g(x)dx=int_(0)^(a)f(x)dx

If f'(x)=(1)/(1+x^(2)) for all x and f(0)=0 , show that 0.4 lt f (2) lt2

The function f(x)= {(5x-4 ", " 0 lt x le 1 ),( 4x^3-3x", " 1 lt x lt 2):}

MOTION-AREA UNDER THE CURVE-EXERCISE - 2 (LEVEL-I)
  1. The area bonunded by the curve y = sin2x, axis and y=1, is

    Text Solution

    |

  2. The area between the curve y = sec x and y-axis when 1le y le 2 is-

    Text Solution

    |

  3. If the area bounded by the x-axis, the curve y=f(x), (f(x)gt0)" and th...

    Text Solution

    |

  4. The area bounded by the curves 1y = x(1 – nx) , x = e^(–1) and positi...

    Text Solution

    |

  5. Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs in...

    Text Solution

    |

  6. The area bounded by the curves y=-sqrt(-x) and x=-sqrt(-y) where x,yle...

    Text Solution

    |

  7. The area of the region bounded by the curves y= abs(x-1) and y = 3 -ab...

    Text Solution

    |

  8. Aea of the region nclosed between the curves x=y^2-1 and x=|y|sqrt(1-y...

    Text Solution

    |

  9. Area enclosed by the curves y= "lnx" , y = lnabs(x),y= abs(lnx)and y =...

    Text Solution

    |

  10. Let y = g(x) be the inverse of a bijective mapping f : R rarr R f(x) =...

    Text Solution

    |

  11. The value of a(agt0) for which the area bounded by the curves y=(x)/(6...

    Text Solution

    |

  12. If the tangent to the curve y = 1 – x^(2) at x = alpha, where 0 lt alp...

    Text Solution

    |

  13. Let 'a' be a positive constant number. Consider two curves C1: y=e^x...

    Text Solution

    |

  14. A function y=f(x) satisfies the differential equation (dy)/(dx)-y= co...

    Text Solution

    |

  15. The parabolas y^(2)=4x and x^(2)=4y divide the square region bounded b...

    Text Solution

    |

  16. Let f be a non-negative continuous function such that the area bounded...

    Text Solution

    |

  17. y=f(x) is a function which satisfies f(0)=0, f"''(x)=f'(x) and f'(0)=1...

    Text Solution

    |

  18. Suppose g(x) = 2x + 1 and h(x) = 4x^(2) + 4x + 5 and h(x) = (fog)(x). ...

    Text Solution

    |

  19. Let f(x) = x^(2) + 6x + 1 and R denote the set of points (x, y) in the...

    Text Solution

    |

  20. A point P moves inside a triangle formed by A(0, 0), B(2, 2sqrt(3) ), ...

    Text Solution

    |