Home
Class 12
MATHS
IfI=int0^((3pi)/5)(1+x)sinx+(1-x)cosx)dx...

`IfI=int_0^((3pi)/5)(1+x)sinx+(1-x)cosx)dx ,` then value of `(sqrt(2)-1)I` is_____

Text Solution

Verified by Experts

The correct Answer is:
2
`I=int_(0)^(3pi//4) (sinx+cosx)dx+int_(0)^(3pi//4)ubrace(x)_(1)ubrace((sinx-cosx))_(II)dx`
`=int_(0)^(3pi//4) (sinx+cosx)dx+ubrace(x(-cosx-sinx)|_(0)^(3pi//4))_("zero")`
`+int_(0)^(3pi//4) (sinx+cosx)dt`
`=2int_(0)^(3pi//4)(sinx+cosx)dx=2sqrt(2)+1`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Main Previous Year|12 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Matrix)|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^2x)/(sinx+cosx)dx

Evaluate : int_0^(pi/2) (sinx+cosx) dx

int_(0)^(pi)(cosx)/(1+sinx)dx=

Evaluate: int_(0)^(pi/4)(1)/(sinx+cosx) dx.

Evaluate: inte^x((1-sinx)/(1-cosx))dx

Evaluate: int_0^(pi/2)|sinx-cosx|dx

Evaluate int_(0)^((pi)/2)(sin3x)/(sinx+cosx) dx .

If int_(0)^(4pi)ln|13sinx+3sqrt3cosx|dx=kpiln7 , then the value of k is

Evaluate int_(0)^(pi/2)sinx/(cosx+sinx)dx .

Evaluate int_(0)^(pi/2)(sinx/(cosx+sinx))dx

CENGAGE-DEFINITE INTEGRATION -Exercise (Numerical)
  1. A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint0...

    Text Solution

    |

  2. Consider the polynomial f(x)=a x^2+b x+cdot If f(0),f(2)=2, then the m...

    Text Solution

    |

  3. IfI=int0^((3pi)/5)(1+x)sinx+(1-x)cosx)dx , then value of (sqrt(2)-1)I...

    Text Solution

    |

  4. If int(0)^(100) f(x)dx=7, then sum(r=1)^(100)int(0)^(1)(r-1+x)dx=.

    Text Solution

    |

  5. The value of int0^((3pi)/2)(|tan^(-1)tanx|-|sin^(-1)sinx|)/(|tan^(-1)t...

    Text Solution

    |

  6. L e tf(x)=x^3=(3x^2)/2+x+1/4 Then the value of (int(1/4)^(3/4)f(f(x))...

    Text Solution

    |

  7. The value of int(0)^(1)(tan^(-1)x)/(cot^(-1)(1-x+x^(2))dx is.

    Text Solution

    |

  8. Let f(x) be differentiate function symmetric about x=2, then the value...

    Text Solution

    |

  9. Let f:[0,oo)vecR be a continuous strictly increasing function, such th...

    Text Solution

    |

  10. If f is continuous function and F(x)=int0^x((2t+3)dotintt^2f(u)d u)dt ...

    Text Solution

    |

  11. If the value of the definite integral int0^1(sin^(-1)sqrt(x))/(x^2-x+1...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. Let g(x) be differentiable on R and int(sint)^1x^2g(x)dx=(1-sint), wh...

    Text Solution

    |

  14. If int0^oox^(2n+1)dote^(-xdx)=360 , then the value of n is

    Text Solution

    |

  15. Let f(x) be a derivable function satisfying f(x)=int0^x e^tsin(x-t)dt...

    Text Solution

    |

  16. Let f(x)=1/x^2 int0^x (4t^2-2f'(t))dt then find f'(4)

    Text Solution

    |

  17. If the value of the definite integral int0^1^(2007)C7x^(2000)dot(1-x)^...

    Text Solution

    |

  18. IfIn=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))i se q u a lto

    Text Solution

    |

  19. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

    Text Solution

    |

  20. L e tJ=int(-5)^(-4)(3-x^2)tan(3-x^2)dxa n dK=int(-2)^(-1)(6-6x+x^2) t...

    Text Solution

    |