Home
Class 12
MATHS
f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx...

`f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt`
The value of `int_(0)^(pi//2) f(x)dx` is

A

`1`

B

`-2`

C

`-1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|6 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Numerical)|28 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The range of f(x) is

f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt f(x) is not invertible for

int_(0)^(pi/2)e^(-x) sinx dx is

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx

Evaluate : int_0^(pi/2) (sinx+cosx) dx

Find int_((-pi)/(4))^(pi/4)|sinx|dx

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of int_(0)^(pi//2) f(x)dx lies in the interval

Evaluate, int_(0)^(pi//2)(dx)/(5+4sinx) .

Evaluate int_(0)^(pi)(x)/(1+sinx) dx.

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

CENGAGE-DEFINITE INTEGRATION -Exercise (Comprehension)
  1. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

    Text Solution

    |

  2. Evaluate int(0)^(2)(x^2+x+2)dx

    Text Solution

    |

  3. Evaluating integrals dependent on a parameter: Differentiate I with ...

    Text Solution

    |

  4. Evaluate int(2)^(3)(x^2+1)dx

    Text Solution

    |

  5. Evaluating integrals dependent on a parameter: Differentiate I with ...

    Text Solution

    |

  6. Evaluating integrals dependent on a parameter: Differentiate I with ...

    Text Solution

    |

  7. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The range of f(x) is

    Text Solution

    |

  8. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt f(x) is not invertibl...

    Text Solution

    |

  9. f(x)=sinx+int(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The value of int(0)^(...

    Text Solution

    |

  10. Let u=int0^oo (dx)/(x^4+7x^2+1 and v=int0^oo (x^2dx)/(x^4+7x^2+1) then

    Text Solution

    |

  11. Let u=int0^oo (dx)/(x^4+7x^2+1 and v=int0^oo (x^2dx)/(x^4+7x^2+1) then

    Text Solution

    |

  12. If f(x)=int0^1(dt)/(1+|x-t|),t h e nf^(prime)(1/2)i se q u a lto 0 (b...

    Text Solution

    |

  13. If f(x)=int(0)^(1)(dt)/(1+|x-t|),x epsilonR Which of the following ...

    Text Solution

    |

  14. Let f be a differentiable function satisfying int(0)^(f(x))f^(-1)(t)d...

    Text Solution

    |

  15. Let f be a differentiable function satisfying int(0)^(f(x))f^(-1)(t)d...

    Text Solution

    |

  16. If U(n)=int(0)^(pi)(1-cosnx)/(1-cosx)dx where n is positive integer of...

    Text Solution

    |

  17. If Un=int0^pi(1-cosnx)/(1-cosx)dx , where n is positive integer or zer...

    Text Solution

    |

  18. Evaluate int(0)^(2)(2x^2+x+1)dx

    Text Solution

    |

  19. Evaluate int(0)^(4)(x^2+2x+8)dx

    Text Solution

    |

  20. Let the definite integral be defined by the formula int(a)^(b)f(x)dx=(...

    Text Solution

    |