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

A. `1`

B

B. `-2`

C

C. `-1`

D

D. `2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MATRIX MATCH_TYPE|6 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise NUMERICAL VALUE_TYPE|28 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|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) (sin^2x)/(sinx+cosx)dx

Let I= int_(pi//4)^(pi//3) (sinx)/(x)dx . Then

Evaluate int_(0)^(2pi)|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

int_(0)^(pi)(dx)/(3+2sinx+cosx)

int_(0)^(pi)sqrt(1+sinx)dx

y=f(x) satisfies the relation int_(2)^(x)f(t)dt=(x^(2))/2+int_(x)^(2)t^(2)f(t)dt The value of int_(-2)^(2)f(x)dx is

Evaluate int_(0)^(pi//2)|sinx-cosx|dx .

CENGAGE PUBLICATION-DEFINITE INTEGRATION -LC_TYPE
  1. Let f(x) and phi(x) are two continuous function on R satisfying phi(x)...

    Text Solution

    |

  2. Find the area of a parallelogram whose adjacent sides are given by th...

    Text Solution

    |

  3. The value of int(0)^(1)(x^(a)-1)/(logx)dx is

    Text Solution

    |

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

    Text Solution

    |

  5. The value of (dI)/(da) when I=int(0)^(pi//2) log((1+asinx)/(1-asinx)) ...

    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)=int(0)^(1)(dt)/(1+|x-t|),x in R. The value of f'(1//2) is equa...

    Text Solution

    |

  13. If f(x)=int(0)^(1)(dt)/(1+|x-t|),x in R. The value of f'(1//2) is equa...

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

    Text Solution

    |

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

    Text Solution

    |

  18. Assertion : Millikan's experiment established that electric charge is ...

    Text Solution

    |

  19. If p1 and p2 are the lengths of the perpendiculars from the point (2,3...

    Text Solution

    |

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

    Text Solution

    |