Home
Class 12
MATHS
If y(x)=int(pi^2/16)^(x^2)(cosxcossqrt(t...

If `y(x)=int_(pi^2/16)^(x^2)(cosxcossqrt(theta))/(1+sin^2sqrt(theta))d theta`, find `(dy)/(dx)` at `x=pi`.

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

I f f(x)=int_((pi^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta))d theta, then find_the value of f^(prime)(pi/2)dot

int_(0)^((pi)/(2))(sin^(3)theta)/(sin^(3)theta+cos^(3)theta)d theta

int_(0)^(pi)(sin4theta)/(sintheta)d theta=0

If x=2cos theta -cos2 theta and y=2sin theta -sin2 theta , find (d^2y)/(dx^2) at theta=pi/2 .

If x=acos^(3)theta" and "y=bsin^(3)theta , then find (d^(2)y)/(dx^(2)) at theta=(pi)/(4).

If x=a(theta+sin theta) and y=a(1-costheta) , find (d^2y)/(dx^2)"at"theta=pi/2

Evaluate: int_(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a >0

Evaluate: int_(-pi/2)^(pi/2)log((a-sin theta)/(a+sin theta)) d theta,a >0

If x=asec^3theta and y=atan^3theta , find (dy)/(dx) at theta=pi/3dot

If x=-a cos theta and y= a sin theta , find (dy)/(dx) .

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

    Text Solution

    |

  2. Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(s...

    Text Solution

    |

  3. If y(x)=int(pi^2/16)^(x^2)(cosxcossqrt(theta))/(1+sin^2sqrt(theta))d t...

    Text Solution

    |

  4. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

    Text Solution

    |

  5. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

    Text Solution

    |

  6. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

    Text Solution

    |

  7. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

    Text Solution

    |

  8. Show that : pi/6leint0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt2)

    Text Solution

    |

  9. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  10. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

    Text Solution

    |

  11. If alpha=int0^1(e^(9x+3tan^-1x))((12+9x^2)/(1+x^2))dx where tan^-1x t...

    Text Solution

    |

  12. Evaluate int(-4)^(-5)e^((x+5)^(2))dx+3int(1//3)^(2//3)e^(9(x-2/3)^(2))...

    Text Solution

    |

  13. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

    Text Solution

    |

  14. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/x

    Text Solution

    |

  15. If for a real number y ,[y] is the greatest integral function less, th...

    Text Solution

    |

  16. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/(1+x^2)

    Text Solution

    |

  17. If int0^x {int0^u f(t) dt}du is equal to (a) int0^x (x-u) f(u) (b) ...

    Text Solution

    |

  18. Compute the integrals: int(1/e)^e1/xsin(x-1/x)dx

    Text Solution

    |

  19. STATEMENT 1: int0^pixsinxcos^2xdx=pi/2int0^pisinxcos^2x dx. STATEMEN...

    Text Solution

    |

  20. Evaluate: int0^(pi/2)xcosx dx

    Text Solution

    |