Home
Class 12
MATHS
Ify=int0^xf(t)sin{k(x-t)}dt ,t h e np ro...

`Ify=int_0^xf(t)sin{k(x-t)}dt ,t h e np rov et h a t(d^2y)/(dx^2)+k^2y=kf(x)dot`

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

If int_0^ycost^2dt=int_0^(x^2)(sint)/t dx ,t h ep rov et h a t(dy)/(dx)=(2sinx^2)/(xcosy^2)

If y=int_(0)^(x)(t-1)(t-2)^(2)dt , find x for which (dy)/(dx)=0 .

If x^m y^n=(x+y)^(m+n),p rov et h a t(dy)/(dx)=y/xdot

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2

If int_0^xf(t) dt=x+int_x^1 tf(t)dt, then the value of f(1)

If y=sqrt(log{sin((x^2)/3-1)}) , t h e n find (dy)/(dx)dot

If a curve is represented parametrically by the equation x=f(t) and y=g(t)" then prove that "(d^(2)y)/(dx^(2))=-[(g'(t))/(f'(t))]^(3)((d^(2)x)/(dy^(2)))

If x=int_0^y (dt)/sqrt(1+9t^2) and (d^2y)/(dx^2)=ay , then find a

If x= e^(cos2t) and y = e^(sin2t) , then move that (dy)/(dx) = -(ylogx)/(xlogy) .

If x=e^(t)sint and y=e^(t)cost , then the value of (x+y)^(2)(d^(2)y)/(dx^(2))-2x(dy)/(dx) is -

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: int(sqrt(2)-1)^(sqrt(2)+1)((x^2-1))/((x^2+1)^2)dx

    Text Solution

    |

  2. int0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer f...

    Text Solution

    |

  3. Ify=int0^xf(t)sin{k(x-t)}dt ,t h e np rov et h a t(d^2y)/(dx^2)+k^2y=k...

    Text Solution

    |

  4. f(x) is a continuous function for all real values of x and satisfies i...

    Text Solution

    |

  5. If x=int0^y (dt)/sqrt(1+9t^2) and (d^2y)/(dx^2)=ay, then find a

    Text Solution

    |

  6. The value of int(1/e)^tanx(tdt)/(1+t^2)+int(1/e)^cotxdt/(t(1+t^2) is

    Text Solution

    |

  7. Prove that: y=int(1/8)^(sin^2x)sin^(-1)sqrt(t)dt+int(1/8)^(cos^2x)cos^...

    Text Solution

    |

  8. f(x)>0AAx in R and is bounded. If lim(n->oo)[int0^a(f(x)dx)/(f(x)+f(a...

    Text Solution

    |

  9. Evaluate: int1^a xdota^(-[(log)a x])dx ,(a >1)dot

    Text Solution

    |

  10. int0^oo(sin^2x)/(x^2)dx must be same as:

    Text Solution

    |

  11. Evaluate: int1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest...

    Text Solution

    |

  12. If int(0)^(oo) (sinx)/x dx=(pi)/2, then int(0)^(oo) (sin^(3)x)/x dx i...

    Text Solution

    |

  13. Find the value of int(-1)^(1)[x^(2)+{x}]dx, where [.] and {.} denote t...

    Text Solution

    |

  14. int0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,and [dot] den...

    Text Solution

    |

  15. Prove that int0^x[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest in...

    Text Solution

    |

  16. Evaluate: int(-pi/2)^(2pi)[cot^(-1)x]dx , where [dot] denotes the grea...

    Text Solution

    |

  17. f(x) is continuous function for all real values of x and satisfies int...

    Text Solution

    |

  18. Prove that int0^1xe^xdx=1

    Text Solution

    |

  19. I1=int0^(pi/2)ln(sinx)dx ,I2=int(-pi/4)^(pi/4)ln(sinx+cosx)dxdot Then ...

    Text Solution

    |

  20. Prove that int0^oo[n e^(-x)]dx=ln((n^n)/(n !)),w h e r en is a na...

    Text Solution

    |