Home
Class 12
MATHS
Let f(x) be a function satisfying f'(x)...

Let f(x) be a function satisfying `f'(x)=f(x)` with `f(0)=1` and g(x) be a function that satisfies `f(x)+g(x)=x^(2)`. Then the value of the integral `int_(0)^(1) f(x)g(x) dx` is equal to -

A

`e+(e^(2))/(2)+(5)/(2)`

B

`e-(e^(2))/(2)-(5)/(2)`

C

`e+(e^(2))/(2)-(5)/(2)`

D

`e-(e^(2))/(2)-(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 5|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 7|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 6|80 Videos

  • MAXIMA AND MINIMA

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination E|2 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

Similar Questions

Explore conceptually related problems

Let f(x)be a function satisfying f(x)=f(x) with f(0)=1 and 'g' be the function satisfying f(x)=g(x)=x^2 the value of the integral int_0^1f(x)g(x)dx is

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be the function satisfying f(x)+g(x)=x^(2) .Prove that, int_(0)^(1)f(x)g(x)dx=(1)/(2)(2e-e^(2)-3)

Prove that the value of the integral, int_(0)^(2a)(f(x))/(f(x)+f(2a-x))dx is equal to a.

int [f(x)g"(x) - f"(x)g(x)]dx is

If (d)/(dx)f(x)=g(x) , then the value of int_(a)^(b)f(x)g(x)dx is -

Let f:RtoR be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt . Then the value of f(log_(e)5) is

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

Let f be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x^3phi(x) for all x and y when phi (x) is a continuous function then f''(x) is equal to

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 8
  1. If the equation a(n)x^(n)+a(n-1)x^(n-1)+…+a(1)x=0 (a(1) ne 0, n ge 2)...

    Text Solution

    |

  2. If x sin y+y cos x=pi, then the value of y''(0) is -

    Text Solution

    |

  3. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be ...

    Text Solution

    |

  4. The value of int(dx)/(x(x^(7)+1)) is equal to -

    Text Solution

    |

  5. If f(x)=|x-1|, then the value of int(0)^(2)f(x) dx is -

    Text Solution

    |

  6. If I(m)=int(1)^(x)(logx)^(m)dx satisfies the relation I(m)=x(logx)^...

    Text Solution

    |

  7. If int(-(1)/(2))^((1)/(2)) cos x log((1+x)/(1-x))dx=k log2, then the ...

    Text Solution

    |

  8. The value of int cos[2cot^(-1) sqrt((1-x)/(1+x))]dx is equal to -

    Text Solution

    |

  9. If int(sinx)^(1) t^(2) f(t) dt =1-sinx, then the value of f((1)/(sqr...

    Text Solution

    |

  10. If int(cos 4x+1)/(cotx-tan x) dx=k cos 4x+c, then the value of k is...

    Text Solution

    |

  11. The value of integral int(dx)/(sin(x-a)sin(x-b)) is -

    Text Solution

    |

  12. If an antiderivative of f(x) is e^(x) and that of g(x) is cosx, then ...

    Text Solution

    |

  13. The value of int sqrt(e^(x)-1)dx is equal to -

    Text Solution

    |

  14. If I(1)=int sin^(-1)x dx and I(2)=int sin^(-1) sqrt(1-x^(2)) dx th...

    Text Solution

    |

  15. The value of int cos^(-(3)/(7)) x sin^(-(11)/(7)) x dx is equal to -

    Text Solution

    |

  16. The value of int(0)^((pi)/(2)) (2^(sinx)dx)/(2^(sinx)+2^(cosx)) is eq...

    Text Solution

    |

  17. The value of int((pi)/(6))^((pi)/(3)) (dx)/(1+sqrt(tan x)) is equal t...

    Text Solution

    |

  18. The value of int(0)^(pi/2) (sin^(4)x dx)/(sin^(4)x+cos^(4)x) is equa...

    Text Solution

    |

  19. State which of the following is correct : If f(x) is a continuous f...

    Text Solution

    |

  20. The integrating factor of the linear differential equation (1-x^(2))^...

    Text Solution

    |