Home
Class 12
MATHS
If intf(x)*cosxdx=1/2{f(x)}^2+c, then f(...

If `intf(x)*cosxdx=1/2{f(x)}^2+c`, then `f(0)=` (A) `1` (B) `0` (C) `-1` (D) none of these

A

1

B

-1

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|29 Videos

  • INTEGRATION

    TARGET PUBLICATION|Exercise CRITICAL THINKING|179 Videos

  • DIFFERENTIATION

    TARGET PUBLICATION|Exercise EVALUATION TEST|30 Videos

  • LINE

    TARGET PUBLICATION|Exercise Evaluation Test|1 Videos

Similar Questions

Explore conceptually related problems

If intf(x)cosxdx=1/2[f(x)]^(2)+c," then " f(pi/2) is

If intf(x)cos x dx = 1/2 f^(2)(x)+C , then f(x) can be

If a (A) x=0 (B) x=1 (C) x=2 (D) None of these.

If int_0^x f(t)dt=x+int_x^1 t f(t)dt , then f(1)= (A) 1/2 (B) 0 (C) 1 (D) -1/2

If the two roots of the equation (c-1)(x^2+x+1)^2-(c+1)(x^4+x^2+1)=0 and real and distinct and f(x)=(1-x)/(1+x) then f(f(x))+f(f(1/x))= (A) -c (B) c (C) 2c (D) none of these

If intf(x)cosx dx=(1)/(2)=(1)/(2)[f(x)]^(2)+c, then f(x) can be

Let f(x)=max. {2-x,2,1+x} then int_(-1)^1 f(x)dx= (A) 0 (B) 2 (C) 9/2 (D) none of these

If intf(x)sec^(2)xdx=(1)/(2)[f(x)]^(2)+c, then : f(x) can be

If f(x)=(1-cos2x)/(x^(2)) , x!=0 and f(x) is continuous at x=0 ,then f(0)= (a) 1 (b) 2 (c) 3 (d) None of these

TARGET PUBLICATION-INTEGRATION-COMPETITIVE THINKING
  1. समाकलन करें int (xdx)/((x^(2)-a^(2))(x^(2)-b^(2)))dx.

    Text Solution

    |

  2. If : int(2x^(2)+3)/((x^(2)-1)(x^(2)-4))dx=log[((x-2)/(x+))^(a).((x+1)/...

    Text Solution

    |

  3. If : int(2x^(2)+3)/((x^(2)-1)(x^(2)-4))dx=log[((x-2)/(x+))^(a).((x+1)/...

    Text Solution

    |

  4. int(5x^(2)+3)/(x^(2)(x^(2)-2))dx=

    Text Solution

    |

  5. int1/(x^(6)+x^(4))dx is equal to

    Text Solution

    |

  6. int(dx)/(e^(2x)-3e^(x))=

    Text Solution

    |

  7. If int(x)/((x^(2)+1)(x-1))dx =Alogabs(x^(2)+1)+Btan^(-1)x+Clogabs(x-...

    Text Solution

    |

  8. int(2x+3)/((x-1)(x^2+1))dx =loge{(x-1)^(5/2)(x^2+1)^a-1/2 tan^-1 x+C,x...

    Text Solution

    |

  9. int(d x)/(x(x^4+1))=

    Text Solution

    |

  10. int(dx)/(x^(3)+3x^(2)+2x)=

    Text Solution

    |

  11. int(dx)/(sinx+sin2x) का मान ज्ञात कीजिए ।

    Text Solution

    |

  12. If intf(x)/(logcosx)dx=-log(logcosx)+c, then f(x) is equal to

    Text Solution

    |

  13. If int(f(x))/(log(sinx))dx=log[log sinx]+c, then f(x) is equal to

    Text Solution

    |

  14. If intf(x)cosxdx=1/2[f(x)]^(2)+c," then " f(pi/2) is

    Text Solution

    |

  15. If intf(x)*cosxdx=1/2{f(x)}^2+c, then f(0)= (A) 1 (B) 0 (C) -1 (D) non...

    Text Solution

    |

  16. If f'(x)=2-5/x^(4) " and " f(1)=14/3, " then " f(-1)=

    Text Solution

    |

  17. If intf(x)sinxcosxdx=(1)/(2(b^(2)-a^(2)))log{f(x)}+C then f(x) is equ...

    Text Solution

    |

  18. If d/dx[f(x)]=xcosx+sinx " and " f(0)=2, then f(x)=

    Text Solution

    |

  19. If intlog(x^(2)+x)dx=xlog(x^(2)+x)+A, then A=

    Text Solution

    |

  20. If I(1)=intsin^(-1)xdx and I(2)sin^(-1)sqrt(-x^(2))dx, then

    Text Solution

    |