Home
Class 12
MATHS
"I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2...

`"I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c`

A

`a=(sqrt(2))/(5), b=(1)/(sqrt(5))`

B

`a=(sqrt(2))/(5), b=5`

C

`a=(sqrt(2))/(5), b= -(1)/(sqrt(5))`

D

`a=(sqrt(2))/(5), b= sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(dx)/(cos^(3)xsqrt(sin2x))`
`=int(dx)/(cos^(3)xsqrt((2sinx cosx)/(cos^(2)x)cos^(2)x))`
`=int(sec^(4)x)/(sqrt(2tanx))=(1)/(sqrt(2))int(sec^(2)x(1+tan^(2)x))/(sqrt(tanx))dx`
Let `t=sqrt(tanx)`
or `dt=(sec^(2)xdx)/(2sqrt(tanx))`
` :. dt =(2)/(sqrt(2))int(1+t^(4))dt=sqrt(2)(1+(t^(5))/(5))+C`
`=(sqrt(2))/(5) t(t^(4)+5)+C`
`=(sqrt(2))/(5)sqrt(tanx)(tan^(2)x+5)+C`
or `a=(sqrt(2))/(5), b=5`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise Exercises (Multiple Correct Answers Type)|17 Videos

  • INDEFINITE INTEGRATION

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

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.9|15 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE ENGLISH|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

Ifint(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c ,t h e n (a) a=(sqrt(2))/5,b=1/(sqrt(5)) (b) a=(sqrt(2))/5,b=5 (c) a=(sqrt(2))/5,b=-1/(sqrt(5)) (d) a=(sqrt(2))/5, b=sqrt(5)

Evaluate: int(dx)/(cos^3xsqrt(sin2x))

Evaluate: int(dx)/(cos^(3)xsqrt(2sin2x))

Evaluate int(dx)/(cos xsqrt(cos2x)) .

If int(dx)/(3sqrt(sin^(11)x*cosx))=-(a(b+ctan^(2)x))/(d tan^(2)x(tanx)^(2//3))+k , then a+b+c+d equal to

If int(dx)/(sqrt(sin^(3)xcos^(5)x))=a sqrt(cot x)+bsqrt(tan^(3)x)+c, then

int(sec^(2)x)/(sqrt(tanx))dx

Evaluate: (i) int(cos^3x)/(sqrt(sinx))\ dx (ii) int(sin^3x)/(sqrt(cosx)\ )\ dx

int tan(pi/4-x)/(cos^2xsqrt(tan^3x+tan^2x+tanx))dx

Evaluate: int_0^(pi//2)1/(cos^3xsqrt(2sin2x))dx

CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...

    Text Solution

    |

  2. If int(dx)/(sqrt(sin^(3)xcos^(5)x))=a sqrt(cot x)+bsqrt(tan^(3)x)+c, t...

    Text Solution

    |

  3. "I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c

    Text Solution

    |

  4. If int(dx)/((x+2)(x^(2)+1)) = alog|1+x^(2)|+btan^(-1)x+ 1/5log|x+2|+C,...

    Text Solution

    |

  5. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

    Text Solution

    |

  6. If intf(x)sinxcosxdx=1/(2(b^2-a^2))lnf(x)+c ,then f(x) is equal to

    Text Solution

    |

  7. int(x^(9))/((4x^(2)+ 1)^(6))dx is equal to

    Text Solution

    |

  8. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b , th...

    Text Solution

    |

  9. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

    Text Solution

    |

  10. int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3...

    Text Solution

    |

  11. If I=int (dx)/((a^(2)-b^(2)x^(2))^(3//2)), then I equals

    Text Solution

    |

  12. int((x^4-1)dx)/(x^2sqrt(x^4+x^2+1))

    Text Solution

    |

  13. int(sqrt(x^2+1))/(x^4)dx=

    Text Solution

    |

  14. int (1+2x^(6))/((1-x^(6))^(3//2))dx is equal to

    Text Solution

    |

  15. The integral int[2x^[12]+5x^9]/[x^5+x^3+1]^3.dx is equal to-

    Text Solution

    |

  16. If In=int( lnx)^n dx then In+nI(n-1)

    Text Solution

    |

  17. int e^x {f(x)-f'(x)}dx= phi(x), then int e^x f(x) dx is

    Text Solution

    |

  18. For x >1,int sin^(- 1)((2x)/(1+x^2))dx is equal to

    Text Solution

    |

  19. If int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)) dx=asqrt(1+x^2)ln(x+sqrt(1+x...

    Text Solution

    |

  20. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

    Text Solution

    |