Home
Class 12
MATHS
Ifx=int0^y(dt)/(sqrt(1+9t^2))a n d(d^2y)...

`Ifx=int_0^y(dt)/(sqrt(1+9t^2))a n d(d^2y)/(dx^2)=a y ,t h e nfin da`

Text Solution

Verified by Experts

`x=int_(0)^(y)(dt)/(sqrt(1+9t^(2)))`
Differentiating w.r.t `y`, we get
`(dx)/(dy)=1/(sqrt(1+9y^(2)))`
or `(dy)/(dx)=sqrt(1+9y^(2))`
or `d/(dx)((dy)/(dx))=d/(dy)(sqrt(1+9y^(2)))(dy)/(dx)`
or `(d^(2)y)/(dx^(2))=(18y)/(2sqrt(1+9y^(2)))sqrt(1+9y^(2))=9y`
or `a=9`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.1|4 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 8.2|17 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

x y=(x+y)6na n d(dy)/(dx)=y/x t h e nn= 1 b. 2 c. 3 d. 4

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

Ifint_0^(npi)f(cos^2x)dx=kint_0^pif(c0s^2x)dx ,t h e nfin dt h ev a l u ekdot

Ifx=int_c^(sint)sin^(-1)z dz ,y=int_k^(sqrt(t))(sinz^2)/zdz ,t h e n(dy)/(dx)i se q u a lto (tant)/(2t) (b) (tant)/(t^2) (c) tan t/(2t^2) (d) (t a tt^2)/(2t^2)

Find (d^2y)/(dx^2) if x = at^2 , y=2 "at", t ne 0

If m, n are the order and degree of the differential equation [(d^(4)y)/(dx^(4))+(d^(2)y)/(dx^(2))]^((1)/(2))=a(d^(2)y)/(dx^(2)) respectively, then the value of 4m-n is

Iff(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int_0^1f(x)dx=(2A)/pi,t h e ncon s t a n t sAa n dBa r e pi/2a n dpi/2 (b) 2/pia n d3/pi 0a n d-4/pi (d) 4/pia n d0

If sin^(-1)((x^2-y^2)/(x^2+y^2))=loga ,t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2-y^2)/(x^2+y^2) (d) y/x

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2

y = e^(ax) then (d^(n)y)/(dx^(n)) = y_(n) is:

CENGAGE-DEFINITE INTEGRATION -JEE Advanced Previous Year
  1. Ifx=int0^y(dt)/(sqrt(1+9t^2))a n d(d^2y)/(dx^2)=a y ,t h e nfin da

    Text Solution

    |

  2. Solve: (x+2)^3=2x(x^2-1)

    Text Solution

    |

  3. The value of int0^1(x^4(1-x)^4)/(1+x^2)\ dx is

    Text Solution

    |

  4. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  5. Find the roots of the following quadratic equations x^2-2x-3

    Text Solution

    |

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

    Text Solution

    |

  7. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  8. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  9. int((pi)/4)^((pi)/2)(2cosecx)^17 dx

    Text Solution

    |

  10. Find A × B, A × A and B × A : A = {1, 2, 3} and B = {1, −4}.

    Text Solution

    |

  11. Evaluate: int(-pi//2)^(pi//2)(cosx)/(1+e^x)dx

    Text Solution

    |

  12. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

    Text Solution

    |

  15. For a in R (the set of all real numbers), a!=-1), (lim)(nvecoo)((1^a...

    Text Solution

    |

  16. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

    Text Solution

    |

  17. Let f:(0,oo) in R be given f(x)=overset(x)underset(1//x)int e^-(t+(1...

    Text Solution

    |

  18. The option(s) with the values of aa n dL that satisfy the following eq...

    Text Solution

    |

  19. Given A = {2,4,5 }, B = {2, 5}, C = {3, 4} and D = {1, 3, 5}, check if...

    Text Solution

    |

  20. ("lim")(xvecoo)((n^2)/(n^2))^(n(n-1)i se q u a lto e (b) e^2 (c) e^(...

    Text Solution

    |

  21. Let f: RvecR be a continuous function which satisfies f(x)= int0^xf(t...

    Text Solution

    |