Home
Class 12
MATHS
If intsin^(-1)xcos^(-1)xdx=f^(-1)(x) [π...

If `intsin^(-1)xcos^(-1)xdx=f^(-1)(x)` `[π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+C ,t h e n` `f(x)=sinx` (b) `f(x)=cosx` `A=pi/4` (d) `A=pi/2`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

If int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1)+B F(x-4)+C and F(x)=int(e^x)/xdx ,t h e n

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xy(x)= 1 (b) -1 (c) 0 (d) none of these

If f(x)=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)f^(x)-xf(x)= (a)1 (b) -1 (c) 0 (d) none of these

If f(x)=cos^2x+s e c^2x ,t h e n f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1 (d) """"f(x)ge2

If f(x)=cos^2x+s e c^2x ,t h e n (a) f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1 (d) """"f(x)ge2

If f(x)=cos^(-1)((2x^2+1)/(x^2+1)), then rang of f(x) is [0,pi] (2) (0,pi/4] (0,pi/3] (4) [0,pi/2)

Let f(x) = tan x, x in (-pi/2,pi/2)and g(x) = sqrt(1-x^2) then g(f(x)) is

Find the domain of the following following functions: (a) f(x)=(sin^(-1))/(x) (b) f(x)=sin^(-1)(|x-1|-2) (c ) f(x)=cos^(-1)(1+3x+2x^(2)) (d ) f(x)=(sin^(-1)(x-3))/(sqrt(9-x^(2))) (e ) f(x)="cos"^(-1)((6-3x)/(4))+"cosec"^(-1)((x-1)/(2)) (f) f(x)=sqrt("sec"^(-1)((2-|x|)/(4)))

If f: R^+ to R , f(x) + 3x f(1/x)= 2(x+1),t h e n find f(x)

If inte^(sinx).(xcos^(3)x-sinx)/(cos^(2)x)dx=e^(sinx)f(x)+C , such that f(0) =-1 then pi/3-f(pi/3) is equal to:

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c, then (a) f(x) is an ...

    Text Solution

    |

  2. Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n both f...

    Text Solution

    |

  3. If intsin^(-1)xcos^(-1)xdx=f^(-1)(x) [π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2...

    Text Solution

    |

  4. If int(cos4x+1)/(cotx-tanx)dx = Acos4x+B ,t h e n (a)A=-1/8 (b) B=1/...

    Text Solution

    |

  5. Statement 1: int(dx)/(x^3sqrt(1+x^4))=-1/2sqrt(1+1/(x^4))+C Statement...

    Text Solution

    |

  6. Statement 1: int(sinxdx)/x ,(x >0), cannot be evaluated. Statement 2:...

    Text Solution

    |

  7. int(4e^x+6e^(-x))/(9e^x-4e^(-x))dx=A x+Blog(9e^(2x)-4)+C ,t h e n A= ...

    Text Solution

    |

  8. The value of the integral int(cos^3x+cos^5x)/(sin^2x+sin^4x)dxi s si...

    Text Solution

    |

  9. Evaluate: intsin^(-1)((2x+2)/(sqrt(4x^2+8x+13)))dx

    Text Solution

    |

  10. Evaluate: for m in N , intx^(3m)+x^(2n)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx...

    Text Solution

    |

  11. Evaluate: int(cos^4x)/(sin^3x(sin^5x+cos^5x)^(3/5))dx

    Text Solution

    |

  12. Evaluate: int sqrt(1+cosec x) dx ,(0 < x < pi/2)

    Text Solution

    |

  13. int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1...

    Text Solution

    |

  14. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

    Text Solution

    |

  15. Evaluate: int(dx)/(x^3sqrt(x^2-1))

    Text Solution

    |

  16. Evaluate : int(2x)/((1-x^2)sqrt(x^4-1))dx

    Text Solution

    |

  17. Evaluate: intsqrt(secx-1)dx

    Text Solution

    |

  18. Evaluate: intsqrt((3-x)/(3+x))sin^(-1)(1/6sqrt(3-x))dx

    Text Solution

    |

  19. Evaluate: int((1-xsinx)dx)/(x(1-x^3e^(3cosx)))

    Text Solution

    |

  20. Evaluate: If intcos^nxdotdx prove that In=1/n(cos^(n-1)xsinx)+((n-1)/n...

    Text Solution

    |