Home
Class 12
MATHS
If intsinx d(secx)=f(x)-g(x)+c ,t h e n ...

If `intsinx d(secx)=f(x)-g(x)+c ,t h e n` `f(x)=secx` (b) `f(x)=tanx` `g(x)=2x` (d) `g(x)=x`

A

`f(x)=secx`

B

`f(x)=tanx`

C

`g(x)=2x`

D

`g(x)=x`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`int sinx d(secx)=int sinx(d(secx))/(dx)dx`
`=int sinx secx tan x dx`
`=int tan^(2)x dx`
`=int(sec^(2)x-1)dx`
`=tanx-x+C`
` :. f(x)=tanx,g(x)=x`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Exercises (Linked Comprehension Type)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXERCISES (Matrix Match Type)|4 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise EXERCISES (Single Correct Answer Type)|77 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

If (d)/(dx)f(x)=g(x) , then the value of int_(a)^(b)f(x)g(x)dx is -

If intsin^(-1)xcos^(-1)xdx=f^(-1)(x)[π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2x+C ,t h e n (a) f(x)=sinx (b) f(x)=cosx (c) f(x)=tanx (d) none of these

If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then a) f(x)=sin^2x ,g(x)=sqrt(x) b) f(x)=sinx ,g(x)=|x| c) f(x=x^2,g(x)=sinsqrt(x) d) fa n dg cannot be determined

int [f(x)g"(x) - f"(x)g(x)]dx is

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=1/x ,g(x)=1/(x^2), and h(x)=x^2 , then (A) f(g(x))=x^2,x!=0,h(g(x))=1/(x^2) (B) h(g(x))=1/(x^2),x!=0,fog(x)=x^2 (C) fog(x)=x^2,x!=0,h(g(x))=(g(x))^2,x!=0 (D) none of these

f(x)=e^x.g(x) , g(0)=2 and g'(0)=1 then f'(0)=

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n a) both f(x)a n dg(x) are odd functions b) f(x) is monotonic function c) f(x)=g(x) has no real roots d) int(f(x))/(g(x))dx=-1/x+3/(x^3)+c

If f(x)=sinx, g(x)=x^2 and h(x)=log x, find h[g{f(x)}].

CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Exercises (Multiple Correct Answers Type)
  1. Evaluate:int(dx)/(sqrt(2e^(x)-1))=

    Text Solution

    |

  2. If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x...

    Text Solution

    |

  3. Evaluate: int sqrt(1+cosecx dx)

    Text Solution

    |

  4. If I=intsec^2xcos e c^4x dx=Acot^3x+Btanx+Ccotx+D , then find the valu...

    Text Solution

    |

  5. A curve g(x)=intx^(27)(1+x+x^2)^6(6x^2+5x+4)dx is passing through orig...

    Text Solution

    |

  6. If int (sqrtx)^5/((sqrtx)^7+x^6) dx= alog(x^k/(1+x^k))+c then a and k ...

    Text Solution

    |

  7. If I=int(sinx+sin^3x)/(cos2x)dx=Pcosx+Qlog|f(x)|+R , then P=1/2,Q=-3/(...

    Text Solution

    |

  8. 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)...

    Text Solution

    |

  9. If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b...

    Text Solution

    |

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

    Text Solution

    |

  11. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. If f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n f(x) is an odd f...

    Text Solution

    |

  15. If int(dx)/(x^2+a x+1)=f(g(x))+c , then f(x) is inverse trigonometric ...

    Text Solution

    |

  16. If int((1-x^7))/(x(1+x^7))dx=Plogabsx+Qlogabs(x^7+1)+c

    Text Solution

    |

  17. If int (3sinx+2cosx)/ (3cosx+2sinx) dx=a x+b ln|2sinx+3cosx|+C, then (...

    Text Solution

    |