Home
Class 12
MATHS
If A=int0^pi cosx/(x+2)^2 \ dx, then int...

If `A=int_0^pi cosx/(x+2)^2 \ dx`, then `int_0^(pi//2) (sin 2x)/(x+1) \ dx` is equal to

A

`1/2+1/(pi+2)-A`

B

`1/(pi+2)-A`

C

`1+1/(pi+2)-A`

D

`A-1/2-1/(pi+2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int_(0)^(pi//2) (sin 2x)/(x+1)dx`. Put `x=y//2`. Then
`I=int_(0)^(pi)(siny)/(y+2)dy`
`=((-cosy)/(y+2))_(2)^(pi)-int_(0)^(pi) (cosy)/((y+2)^(2))dy` (Integrating by parts)
`1/(pi+2)+1/2-A`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.11|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

int_0^(pi/2) sin x dx

If A=int_(0)^( pi)(cos x)/((x+2)^(2))dx, then int_(0)^( pi/2)(sin2x)/(x+1)dx is equal to

If A= int _(0)^(pi) (sin x)/(x ^(2))dx, then int _(0)^(pi//2) (cos 2 x )/(x) dt is equal to:

int_0^(2pi)(sin2x)dx

int_0^(2pi)(sin2x)dx

int _(0)^(2pi) (sin x + |sin x|)dx is equal to

If A=int_(0)^( pi)(sin x)/(x^(2))dx, then int_(0)^((pi)/(2))(cos(2x))/(x)dx, is equal to:

IfA=int_(0)^( pi)(cos x)/((x+2)^(2))*dx, then int_(0)^((pi)/(2))(sin(2x))/(x+1)*dx is equal to

int_0^(pi/2) sin x sin 2x dx

CENGAGE-DEFINITE INTEGRATION -Exercise (Single)
  1. lim(xto oo) (int(0)^(x)tan^(-1)dt)/(sqrt(x^(2)+1)) is equal to

    Text Solution

    |

  2. A function f is defined by f(x) = int0^pi cos t cos(x-t)dt,0 <= x <= 2...

    Text Solution

    |

  3. If f' is a differentiable function satisfying f(x)=int(0)^(x)sqrt(1-f^...

    Text Solution

    |

  4. If int 0^1e^(x^2)(x-alpha)dx=0, then

    Text Solution

    |

  5. The value of the integral int0^1e^x^2dx lies in the interval (0,1) ...

    Text Solution

    |

  6. Given that f satisfies |f(u)-f(v)|lt=|u-v|forua n dv in [a , b]dot The...

    Text Solution

    |

  7. The value of the integral int0^oo(xlogx)/((1+x^2)^2)dxi s 0 (b) log ...

    Text Solution

    |

  8. int0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdxi se q u a lto -pi/21npi (b) ...

    Text Solution

    |

  9. If A=int0^pi cosx/(x+2)^2 \ dx, then int0^(pi//2) (sin 2x)/(x+1) \ dx ...

    Text Solution

    |

  10. int(0)^(4)((y^(2)-4y+5)sin(y-2)dy)/([2y^(2)-8y+1]) is equal to

    Text Solution

    |

  11. int(sin theta)^(cos theta) f(x tan theta)dx (where theta!=(npi)/2,n ep...

    Text Solution

    |

  12. If I1=int0^1(e^x)/(1+x) dxaand I2=int0^1 x^2/(e^(x^3)(2-x^3)) dx then ...

    Text Solution

    |

  13. L e tI1=int(-2)^2(x^6+3x^5+7x^4)/(x^4+2)dxa n d I2=int(-3)^1(2(x+1)^2...

    Text Solution

    |

  14. Let f beintegrable over [0,a] for any real value of a. If I(1)=int(0...

    Text Solution

    |

  15. The value of inta^b(x-a)^3(b-x)^4dxi s ((b-a)^4)/(6^4) (b) ((b-a)^8)...

    Text Solution

    |

  16. If I(m,n)=int0^1x^(m-1)(1-x)^(n-1)dx, then

    Text Solution

    |

  17. T h ev a l u eoft h ed efin i t ein t egr a lint0^(pi/2)(sin5x)/(sinx)...

    Text Solution

    |

  18. If In=int0^pi e^x(sinx)^n dx , then (I3)/(I1) is equal to

    Text Solution

    |

  19. If f'(x)=f(x)+int(0)^(1)f(x)dx,given f(0)=1, then the value of f(log(e...

    Text Solution

    |

  20. Let f(x) be positive, continuous, and differentiable on the interval ...

    Text Solution

    |