Home
Class 12
MATHS
If I=int0^((3pi)/4)[(1+x)sinx+(1-x)cosx]...

If `I=int_0^((3pi)/4)[(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 PUBLICATION|Exercise JEE MAIN|12 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise JEE ADVANCED|38 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MATRIX MATCH_TYPE|6 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

int_(0)^((pi)/(2))(cosx-sinx)/(1+sinxcosx)dx

int_(0)^(pi)sqrt(1+sinx)dx

If I= int_0^(100pi) sqrt(1-cos2x)dx then the value I is :

int _0^(pi/2) (sin^2x)/(sinx+cosx)dx

if I_10=int_0^(pi/2) x^(10) sinx dx then the value of I_10 + 90 I_8 is

Let I=int_((pi)/(4))^((pi)/(3))(sinx)/(x)dx . Then

If M=int_0^((pi)/(2))(cosx)/(x+2)dx,N=int_0^((pi)/(4))(sinxcosx)/((x+1)^2)dx , then the value of M-N is

If I= int_0^(pi/2) dx/(sqrt(1+sin^3x) then

If int_(0)^(pi) x f(sinx) dx=A int_(0)^((pi)/(2))f(sinx)dx , then the value of A is -

int e^(x).(1+sinx)/(1+cosx)dx

CENGAGE PUBLICATION-DEFINITE INTEGRATION -NUMERICAL VALUE_TYPE
  1. A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint0^...

    Text Solution

    |

  2. Consider the polynomial f(x)=a x^2+b x+c dot If f(0)=0,f(2)=2, then th...

    Text Solution

    |

  3. If I=int0^((3pi)/4)[(1+x)sinx+(1-x)cosx]dx , then value of (sqrt(2)-1...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

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

    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 a differentiable function symmetric about x=2, then the va...

    Text Solution

    |

  9. Let f:[0,oo) to R be a continuous strictly increasing function, such t...

    Text Solution

    |

  10. If f is continuous function and F(x)=int0^x((2t+3)*intt^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. Let f(x)=int(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x...

    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 int4^x (4t^2-2f'(t))dt then find the value of 9f'(4)

    Text Solution

    |

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

    Text Solution

    |

  18. If In=int0^1(1-x^5)^n dx ,t h e n(55)/7(I(10))/(I(11))is equal to

    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)dx and K=int(-2)^(-1)(6-6x+x^2) t...

    Text Solution

    |