Home
Class 12
MATHS
If I(1)= int(0)^(pi//2) x sin x dx and I...

If `I_(1)= int_(0)^(pi//2)` x sin x dx and `I_(2)=int_(0)^(pi//2)` x cos x dx, then which one of the following is true ?

A

`I_(1)+I_(2)=(pi)/(2)`

B

`I_(1)=(pi)/(2)I_(2)`

C

`I_(1)+I_(2)=0`

D

`I_(1)=I_(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • KARNATAKA CET 2005

    KCET PREVIOUS YEAR PAPERS|Exercise MATHEMATICS|59 Videos

  • KARNATAKA CET 2007

    KCET PREVIOUS YEAR PAPERS|Exercise MATHEMATICS|59 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(pi//2) log sin x dx =

int_(0)^(pi//2) cos 2x dx .

int_(0)^(pi//4) cos^(2) x dx

int_(0)^(pi/6) sin2x . cosx dx

If I_(1) = underset(0)overset(pi//2)int x.sin xdx and I_(20 = underset(0)overset(pi//2)(int) x.cos x dx then which one of the following is true?

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

int_(0)^(pi) log(1 + cos x)dx .

If int_0^(pi) x f (sin x) dx = A int_0^(pi//2) f (sin x) dx , then A is :

KCET PREVIOUS YEAR PAPERS-KARNATAKA CET 2006-MATHEMATICS
  1. If the curve y=2x^(3)+ax^(2)+bx+c passes through the origin and the ta...

    Text Solution

    |

  2. A circular sector of perimeter 60 metre with maximum area is to be con...

    Text Solution

    |

  3. The tangent and the normal drawn to the curve y=x^(2)-x+4 at P(1,4) c...

    Text Solution

    |

  4. int((x^(3)+3x^(2)+3x+1))/((x+1)^(5))dx=

    Text Solution

    |

  5. int(cosec x)/(cos^(2)(1+"log tan"(x)/(2)))dx=

    Text Solution

    |

  6. The complex number ((-sqrt(3)+3i)(1-i))/((3+sqrt(3)i)(i)(sqrt(3)+sqrt(...

    Text Solution

    |

  7. If 2x=-1+sqrt(3)i, then the value of (1-x^(2)+x)^(6)-(1-x+x^(2))^(6)=

    Text Solution

    |

  8. The modulus of amplitude of (1+i sqrt(3))^(8) are respectively

    Text Solution

    |

  9. The value of lim(x to 0)(5^(x)-5^(-x))/(2x)=

    Text Solution

    |

  10. Which one of the following is not true always?

    Text Solution

    |

  11. int (dx)/(x sqrt(x^(6)-16))=

    Text Solution

    |

  12. If I(1)= int(0)^(pi//2) x sin x dx and I(2)=int(0)^(pi//2) x cos x dx,...

    Text Solution

    |

  13. If f (x) is defined [-2, 2] by f(x)=4x^(2)-3x+1 and g(x)=(f(-x)-f(x))...

    Text Solution

    |

  14. The area enclosed between the parabola y=x^(2)-x+2 and the line y=x+2 ...

    Text Solution

    |

  15. The solution of the differential equation e^(-x)(y+1)dy+(cos^(2)x -sin...

    Text Solution

    |

  16. If y=1+(1)/(x)+(1)/(x^(2))+(1)/(x^(3))+… to oo with |x|gt 1 then (dy)/...

    Text Solution

    |

  17. If f (x) and g (x) are two functions with g(x)=x-(1)/(x) and fog (x)=x...

    Text Solution

    |

  18. The derivative of a^(sec x) w.r.t. a^(tan x)(a gt 0) is

    Text Solution

    |

  19. If sin(x+y)+cos (x+y)=log(x+y), then (d^(2)y)/(dx^(2))=

    Text Solution

    |

  20. If f (x) is a function such that f''(x)+f(x)=0 and g(x)=[f(x)]^(2)+[f'...

    Text Solution

    |