Home
Class 12
MATHS
Let I=int0^1 (sinx)/sqrtx dx and J=int0^...

Let `I=int_0^1 (sinx)/sqrtx dx and J=int_0^1 (cos x)/sqrtx dx`. Then which of the following is true?

A

`I gt 2/3 and J lt 2`

B

`I gt 2/3 and J gt 2`

C

`I lt 2/3 and J lt 2`

D

`I lt 2/3 and J gt 2`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • DIFFERENTIAL EQUATIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

  • INVERSE - TRIGONOMETRIC FUNCTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST (2)|11 Videos

Similar Questions

Explore conceptually related problems

Let I=int_(0)^(1)(sin)/(sqrt(x))dx and J=int_(0)^(1)(cos x)/(sqrt(x))dx Then which one of the following is true? (1) I>(2)/(3) and j>2(2)I 2(4)I>(2)/(3) and j<2

Let I=int_(0)^(1) (sin x)/(sqrt(x))dx and I=int_(0)^(1) (cos x)/(sqrt(x))int dx . Then, which one of the following is true?

int (cossqrtx)/(sqrtx)dx

int_0^1e^sqrtx/sqrtxdx=

int cos sqrtx dx =…..

int(1-cossqrtx)/(sqrtx)dx=

int(sec sqrtx)/(sqrtx)dx=

inte^(sqrtx)dx

MODERN PUBLICATION-INTEGRALS-COMPETITION FILE
  1. Let I=int0^1 (sinx)/sqrtx dx and J=int0^1 (cos x)/sqrtx dx. Then which...

    Text Solution

    |

  2. The value of sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx , is

    Text Solution

    |

  3. int(0)^(pi)[cotx]dx, where [.] denotes the greatest integer function, ...

    Text Solution

    |

  4. Let p(x) be a function defined on R such that p'(x)=p'(1-x) for all x ...

    Text Solution

    |

  5. The value of int0^1 (8log(1+x))/(1+x^2) dxis:

    Text Solution

    |

  6. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

    Text Solution

    |

  7. Let [] denote the greatest integet function then the value int0^1.5 x[...

    Text Solution

    |

  8. If the integral int (5 tanx)/(tanx-2) dx=x+a log |sin x-2 cosx|+c, the...

    Text Solution

    |

  9. If g(x)=int(0)^(x)cos^(4)t dt, then g(x+pi) equals

    Text Solution

    |

  10. If int f(x)dx=psi(x), then int x^5f(x^3)dx

    Text Solution

    |

  11. The intercepts on x-axis made by tangents to the curve, y=int0^x|t|...

    Text Solution

    |

  12. The integral int(1+x-1/x)e^(x+1/x)dx is equal to

    Text Solution

    |

  13. The integral int(0)^(pi)sqrt(1+4"sin"^2(x)/(2)-4"sin"(x)/(2)) dx is e...

    Text Solution

    |

  14. "The integral " int(dx)/(x^(2)(x^(4)+1)^(3//4))" equals"

    Text Solution

    |

  15. The integral int2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx is equal to:...

    Text Solution

    |

  16. The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to ...

    Text Solution

    |

  17. underset (n rarr infty )(lim) [((n+1)(n+2)...3n)/(n^(2n))]^(1//n) is e...

    Text Solution

    |

  18. int(pi//4)^(3pi//4)(dx)/(1+cosx) is equal to

    Text Solution

    |

  19. Let In=int tan^n x dx, (n>1). If I4+I6=a tan^5 x + bx^5 + C, Where C...

    Text Solution

    |

  20. The integral int(sin^(2)xcos^(2)x)/(sin^(5)x+cos^(3)xsin^(2)x+sin^(3...

    Text Solution

    |