Home
Class 12
MATHS
If f(pi)=2 and int(0)^(pi)(f(x)+f''(x))s...

If `f(pi)=2` and `int_(0)^(pi)(f(x)+f''(x))sin x dx=5`, then `f(0)` is equal to ( it is given that `f(x)` is continuous in `[0,pi]`)

A

7

B

3

C

5

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|103 Videos

  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos

  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

If f(pi) = 2 int_0^pi (f(x)+f^(x)) sinx dx=5 , then f(0) is equal to (it is given that f(x) is continuous in [0,pi]) . (a) 7 (b) 3 (c) 5 (d) 1

If f(x) =int_(0)^(x) sin^(4)t dt , then f(x+2pi) is equal to

Let f(x) = secx*f'(x), f(0) = 1, then f(pi/6) is equal to

int_(0)^(pi//2) ( f ( co x )) /( f (sinx ) + f(co sx) ) dx is equal to

If f'(x) = f(x)+ int _(0)^(1)f (x) dx and given f (0) =1, then int f (x) dx is equal to :

The integral int_(0)^(pi//2) f(sin 2 x)sin x dx is equal to

The integral int_(0)^(pi) x f(sinx )dx is equal to

If int_0^pi x f(sinx) dx=A int_0^(pi/2) f(sinx)dx , then A is (A) pi/2 (B) pi (C) 0 (D) 2pi

If f(x) = int_(0)^(x)(2cos^(2)3t+3sin^(2)3t)dt , f(x+pi) is equal to :

let f(a)=int_(0)^(a)ln(1+tan a tan x)dx then f'((pi)/(4)) equals

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. overset(pi//2)underset(-pi//2)int (cos x)/(1+e^(x))dx=

    Text Solution

    |

  2. int(0)^(2pi)[|sin x|+|cos x|]dx, where [.] denotes the greatest intege...

    Text Solution

    |

  3. If f(pi)=2 and int(0)^(pi)(f(x)+f''(x))sin x dx=5, then f(0) is equal ...

    Text Solution

    |

  4. If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then underset(...

    Text Solution

    |

  5. Evaluate: int0^(4pi)(dx)/(cos^2x(2+tan^2x)

    Text Solution

    |

  6. The value of int(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greate...

    Text Solution

    |

  7. The value of int(1)^(4){x}^([x]) dx (where , [.] and {.} denotes the g...

    Text Solution

    |

  8. If f(x) is continuous for all real values of x , then sum(r=1)^nint0^...

    Text Solution

    |

  9. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

    Text Solution

    |

  10. int(-pi/2)^(pi/2)(e^(|sinx|)cosx)/((1+e^(tanx))dx is equal to e+1 ...

    Text Solution

    |

  11. The value of int(0)^(2)[x^(2)-1]dx, where [x] denotes the greatest in...

    Text Solution

    |

  12. If overset(b)underset(a)int (x^(n))/(x^(4)+(16-x)^(n))dx=6, then

    Text Solution

    |

  13. If af(x)+bf((1)/(x))=(1)/(x)-5,x ne 0,a ne b, then overset(2)underset(...

    Text Solution

    |

  14. Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in...

    Text Solution

    |

  15. The equation int(-pi//4)^(pi//4){a|sin x |+(b sin x )/(1+ cos^(2)+c} d...

    Text Solution

    |

  16. int(1)^(3)|(2-x)log(e )x|dx is equal to:

    Text Solution

    |

  17. overset(pi)underset(0)int (1)/(1+3^(cosx)) dx is equal to

    Text Solution

    |

  18. Let I=int(-a)^(a) (p tan^(3) x + q cos^(2)x + r sin x)dx, where p, q, ...

    Text Solution

    |

  19. The value of int(0)^(100)[tan^(-1)x]dx is, (where [.] denotes greatest...

    Text Solution

    |

  20. The number of value of alpha in the interval [-pi,0] satisfying sin...

    Text Solution

    |