Home
Class 12
MATHS
If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2...

If `int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Psqrt(1-9x^(2))+Q(cos^(-1)3x)^(3)+c` then

A

`P=-(1)/(9)`

B

`Q=-(3)/(8)`

C

`P=(3)/(8)`

D

`Q=-(1)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Promotional Banner

Topper's Solved these Questions

  • INDEFINTE INTEGRAL

    FIITJEE|Exercise COMPREHENSIONS -I|1 Videos
  • INDEFINTE INTEGRAL

    FIITJEE|Exercise COMPREHENSIONS|4 Videos
  • INDEFINTE INTEGRAL

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE LEVEL-I)|51 Videos
  • HYPERBOLA

    FIITJEE|Exercise NUMERICAL BASED|4 Videos
  • MATHEMATICAL REASONING

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-2|18 Videos

Similar Questions

Explore conceptually related problems

If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Asqrt(1-9x^(2))+B(cos^(-1)3x)^(3)+C, then A-B is

int(dx)/(sqrt(1-9x^(2)))

int(x+cos^(-1)x)/(sqrt(1-x^(2)))dx

9. int(cos^(-1)x)^(2)dx

int sqrt(1-9x^(2))dx=?

int( 1)/(sqrt(9x^(2)-1))dx

int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k _(1)) ( sqrt(1-9x ^(2))+ (cos ^(-1) 3x )^(k_(2)))+c, then k _(1) ^(2)+k_(2)^(2)= (where C is an arbitrary constnat. )

int(3x-1)/(sqrt(x^(2)+9))dx

cos^(-1)((x^(2))/(6)+sqrt(1-(x^(2))/(9))sqrt(1-(x^(2))/(4)))=cos^(-1)((x)/(3))-cos^(-1)((x)/(2)) hold for all x belonging to

FIITJEE-INDEFINTE INTEGRAL-ASSIGNMENT PROBLEMS (OBJECTIVE LEVEL-II)
  1. Let f(x)=1/(4-3cos^2x+5sin^2x) and if its antiderivative F(x)=(1/3) ta...

    Text Solution

    |

  2. If I=int(sinx-cosx)/((sinx=cosx)sqrt(sinxcosx+sin^(2)cos^(2))x)dx=cose...

    Text Solution

    |

  3. For x ^ 2 ne n pi + 1, n in N ( the set of natural numb...

    Text Solution

    |

  4. Let f(x)=[b^(2)+(a-1)b+2]x-int(sin^(2)x+cos^(4)x)dx be an increasing f...

    Text Solution

    |

  5. If int((1)/(sin^(2)x))log(cosx+cos2x)dx=cotxlog(cosx+sqrt(cos2x)+P(cos...

    Text Solution

    |

  6. l=int(sin2x)/(8sin^(2)x+17cos^(2)x)dx is equal to

    Text Solution

    |

  7. I=inttan^(2)(2theta)d""theta is equal to

    Text Solution

    |

  8. l(1)=int2^(x)dx=p(x)+c(1)andl(2)=int((1)/(2))^(x)dx=m(x)+c(1) then p(x...

    Text Solution

    |

  9. If int(dx)/(p^(2)sin^(2)x+r^(2)cos^(2)x)=(1)/(12)tan^(-1)(3tanx)+c the...

    Text Solution

    |

  10. int((1+x^(2))(2+x^2))/((xco sx+sinx)^(4))dx equals

    Text Solution

    |

  11. int(dx)/((1+sqrt(x))^8)=

    Text Solution

    |

  12. Iff^(prime)(x)=1/(-x+sqrt(x^2+1))a n df(0)=(1+sqrt(2))/2t h e nf(1) i...

    Text Solution

    |

  13. If int(sinx)/(sin(x-alpha))dx=Ax+Blogsin(x-alpha)+c then

    Text Solution

    |

  14. If intxlog(1+x^(2))dx=A(x).log(1+x^(2))+B(x)+c, then

    Text Solution

    |

  15. If int(sin3theta+sintheta)e^(sintheta)costhetad theta=(Asin^3theta+Bco...

    Text Solution

    |

  16. If int((3x+4))/((x^(3)-2x-4))dx=Alog|x-2|+Blog(f(x))+c, then

    Text Solution

    |

  17. int(dx)/(x^(5//6)(1+5x^(1//3))sqrt(1+4x^(1//3)))

    Text Solution

    |

  18. If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Psqrt(1-9x^(2))+Q(cos^(-...

    Text Solution

    |

  19. If int(dx)/(x^(22)(x^7-6))=A{ln(p)^6+9p^2-2p^3-18 p}+c, then

    Text Solution

    |

  20. intx^(5)cos^(2)logsqrtxdx=

    Text Solution

    |