Home
Class 12
MATHS
Suppose that f,f^prime and f prime prime...

Suppose that `f,f^prime and f prime prime` are continuous on `[0, ln 2]` and that `f (0) = 0, f prime(0) = 3, f(In 2) = 6,f prime(ln 2) = 4 and int_0^(ln 2) e^(-2x)*f(x)dx=3.` Find the value of `int_0^(ln2) e^(-2x)*f prime prime(x)dx.`

Text Solution

Verified by Experts

The correct Answer is:
13
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -2 (LEVEL-I)|97 Videos

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -2 (LEVEL-II)|11 Videos

  • DEFINITE INTEGRATION

    MOTION|Exercise EXERCISE -4 LEVEL-II|33 Videos

  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

  • DETERMINANTS

    MOTION|Exercise EXERCISE-4 (LEVEL-II)|6 Videos

Similar Questions

Explore conceptually related problems

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

f(0)=1 , f(2)=e^2 , f'(x)=f'(2-x) , then find the value of int_0^(2)f(x)dx

Suppose f,f' and f" are continuous on [0,e] and that f^(prime)(e)=f(e)=f(1)=1 and int_1^e(f(x))/(x^2)dx=1/2, then the value of int_1^0 f*(x)ln xdx equals.

If f(a-x)=f(x) and int_(0)^(a//2)f(x)dx=p , then : int_(0)^(a)f(x)dx=

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

Suppose f is continuous, f(0)=0,f(1)=1,f^(prime)(x)>0"and"int_0^1f(x)dx=1/3, Find the value of the definite integral int_0^1f^-1(y)dy.

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

Let f(x)=ae^(2x)+be^x+cx , where f(0)=-1, f'(log_e2)=21 and int_0^(log_e4)(f(x)-cx)dx=39/2 then the value of abs(a+b+c) is__________

Let f:R rarr R be a continuous function with int_(0)^(1)f(x)f'(x)dx=0 and int_(0)^(1)f^(2)(x)f'(x)dx=18 If the value of int_(0)^(1)f^(4)(x)f'(x)dx=(p)/(q) where p and q are relatively prime positive integers,find (p+q)

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

MOTION-DEFINITE INTEGRATION -ELEMENTRAY EXERCISE
  1. Let f(x)=intx^(sinx)(1+xcosxdotlnx+sinx)dxa n df(pi/2)=(pi^2)/4dot The...

    Text Solution

    |

  2. int (0) ^(1) x tan ^(-1) x dx =

    Text Solution

    |

  3. Suppose that f,f^prime and f prime prime are continuous on [0, ln 2] a...

    Text Solution

    |

  4. The value of the integral int(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltal...

    Text Solution

    |

  5. int (a) ^(b) (dx)/( sqrt(1 + x ^(2))) where a = (e-e^(-1))/( 2 ) &b = ...

    Text Solution

    |

  6. int (x^(x)(x^(2x)+1)("ln"x+1))/(x^(4x)+1)dx

    Text Solution

    |

  7. int (0) ^(1) x ^(5) sqrt((1 + x ^(2))/(sqrt(1- x^(2))))dx

    Text Solution

    |

  8. Suppose that the function f, g, f',and g' are continuous over [0,1], g...

    Text Solution

    |

  9. The value of the integral overset(pi//4)underset(0)int (sin theta+cos ...

    Text Solution

    |

  10. int (0) ^(pi) sin ^(2) theta cos theta d theta

    Text Solution

    |

  11. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

    Text Solution

    |

  12. int (0) ^(pi//2) (x + sin x )/(1 + cos x ) dx

    Text Solution

    |

  13. Let A = int (3//4) ^(4//3) (2x ^(2) + x +1 )/( x ^(3) + x ^(2) + x + 1...

    Text Solution

    |

  14. int (2 -x ^(2))/( ( a + 1) (1- x ^(2)))dx

    Text Solution

    |

  15. int(-1)^1(d/dx(1/(1+e^(1/x))))dx

    Text Solution

    |

  16. int (1) ^(e ) (dx )/(ln (x ^(x) e ^(x)))

    Text Solution

    |

  17. int (0) ^(pi)[ cos ^(2) ((3pi)/(8) - (x )/(4)) - cos ^(2) ((11pi)/(8)+...

    Text Solution

    |

  18. If f(pi) =2 and int0^pi (f(x) + f''(x)) sinx dx =5 then f(0) is equal ...

    Text Solution

    |

  19. int (a) ^(b ) (| x |)/(x ) dx

    Text Solution

    |

  20. If f(x)=e^(-x)+2e^(-2x)+3 e^(-3x)+.....+oo, then int(ln2)^(ln3) f(x)dx...

    Text Solution

    |