Home
Class 12
MATHS
Evaluate: int(-1)^3(tan^(-1)x/(x^2+1)+ta...

Evaluate: `int_(-1)^3(tan^(-1)x/(x^2+1)+tan^(-1)(x^2+1)/x)dx`

Text Solution

Verified by Experts

The correct Answer is:
`2pi`
`int_(1)^(3)("tan"^(-1)x/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/x)dx`
`=int_(-1)^(0)("tan"^(-1)x/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/x)dx`
`+int_(0)^(3)("tan"^(-1)x/(x^(2)+1)+"tan"^(-1)(x^(2)+1)/x)dx`
`int_(-1)^(0)-(pi)/2 dx+int_(0)^(3)(pi)/2 dx`
`=[-(pi)/2 x]_(-1)^(0)+[(pi)/2x]_(0)^(3)`
`=2pi`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SCQ_TYPE|113 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLE_TYPE|20 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int_(0)^(1)x^(2)tan^(-1)xdx

Evaluate: int(x^2tan^(-1)x)/(1+x^2)\ dx

Evaluate: int(x^3tan^(-1)x^4)/(1+x^8)dx

Evaluate: int(x^2tan^(-1)x^3)/(1+x^6)dx

Evaluate int_(0)^(1)(tan^(-1)x)/(1+x^(2))dx

Evaluate: int_0^1 tan^-1x/(1+x^2)dx

int_(0)^(1)x(tan^(-1)x)^(2)dx

int_(-1)^(3)[tan^(-1).(x)/(x^(2)+1)+cot^(-1).(x)/(x^(2)+1)]dx

int_(0)^(1)tan^(-1)(1-x+x^(2))dx

Evaluate: int(e^(tan^(-1)x))/((1+x^2))[(sec^(-1)sqrt(1+x^2)+cos^(-1)((1-x^2)/(1+x^2))]dx,(x >0)dot

CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
  1. Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...

    Text Solution

    |

  2. Evaluate int(1)^(5)sqrt((x-2)sqrt(x-1))dx.

    Text Solution

    |

  3. Evaluate: int(-1)^3(tan^(-1)x/(x^2+1)+tan^(-1)(x^2+1)/x)dx

    Text Solution

    |

  4. Evaluate int(1)^(a)x.a^(-[log(a)x])dx,(agt1).Here [.] represents the g...

    Text Solution

    |

  5. Evaluate: int1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest...

    Text Solution

    |

  6. Find the value of int(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot} denot...

    Text Solution

    |

  7. Prove that int0^x[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest in...

    Text Solution

    |

  8. Prove that int0^xf[t]dt=([x]([x]-1))/2+[x](x-[x]), where [.] denotes...

    Text Solution

    |

  9. Evaluate: int0^oo[2e^(-e)]dx ,w h e r e[x] represents greatest intege...

    Text Solution

    |

  10. If f(a+b-x)=f(x), then prove that inta^b xf(x)dx=(a+b)/2inta^bf(x)...

    Text Solution

    |

  11. The value of the integral int3^6 sqrtx/(sqrt(9-x)+sqrtx)dx is

    Text Solution

    |

  12. Find the value of int(0)^(1)root(3)(2x^(3)-3x^(2)-x+1)dx.

    Text Solution

    |

  13. Show that int0^pixf(sinx)dx=pi/2int0^pif(sinx)dxdot

    Text Solution

    |

  14. Find the value of int0^1x(1-x)^ndx

    Text Solution

    |

  15. If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, the...

    Text Solution

    |

  16. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a n ...

    Text Solution

    |

  17. Find the value of int(0)^(pi//2)sin2xlogtanxdx.

    Text Solution

    |

  18. The value of int-pi^pi cos^2x/[1+a^x]dx, a > 0 is

    Text Solution

    |

  19. answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...

    Text Solution

    |

  20. Evaluate int(0)^(pi)(x dx)/(1+cos alpha sin x),where 0lt alpha lt pi.

    Text Solution

    |