Home
Class 12
MATHS
Find the equation of tangent to y=int(x...

Find the equation of tangent to `y=int_(x^2)^(x^3)(dt)/(sqrt(1+t^2))a tx=1.`

Text Solution

Verified by Experts

The correct Answer is:
`sqrt(2)y=x=1`
`y|_(x=1)=0,(dy)/(dx)=1/(sqrt(1+x^(5))) 3x^(2)-1/(sqrt(1+x^(4)))2x`
or `(dy)/(dx)|_(x=1)=1/(sqrt(2))`
Thus, required equation is `ysqrt(2)=x-1`.
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SCQ_TYPE|113 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise SOLVED EXAMPLE_TYPE|20 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Find the equation of tangent to the curve y=sin^(-1)((2x)/(1+x^2)) a tx=sqrt(3)

Find the equation of tangent to the conic x^2-y^2-8x+2y+11=0 at (2,1) .

Find the equation of tangent and normal to the curve x=(2a t^2)/((1+t^2)),y=(2a t^3)/((1+t^2)) at the point for which t=1/2dot

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .

Find the solution for x of the equation int_(2^(1/2))^x1/(t(t^2-1)^(1/2))dt= pi/2 .

Find the equations of the tangent and normal to the curve x^(2/3)+y^((2)/(3))=2 at (1,1).

Evaluate: int(x^(3/2))/(sqrt(1+x^5))dx

Find the equation of tangent to the y = F(x) at x = 1 , where F(x) = underset(x)overset(x^(3))int(dt)/(sqrt(1+t^(2)))

Find the equation of tangents drawn to the parabola y=x^2-3x+2 from the point (1,-1)dot

Evaluate: int(dx)/(x^3sqrt(x^2-1))

CENGAGE PUBLICATION-DEFINITE INTEGRATION -CAE_TYPE
  1. Evaluate (lim)(x to 4)int4^x((4t-f(t)))/((x-4))dt

    Text Solution

    |

  2. Evaluate: lim(xto0)(int(0)^(x^(2))cos^(2)tdt)/(xsinx)

    Text Solution

    |

  3. Find the points of minima for f(x)=int0^x t(t-1)(t-2)dt

    Text Solution

    |

  4. Find the equation of tangent to y=int(x^2)^(x^3)(dt)/(sqrt(1+t^2))a t...

    Text Solution

    |

  5. I f f(x)=int((pi^2)/(16))^(x^2)(sinxsinsqrt(theta))/(1+cos^2sqrt(theta...

    Text Solution

    |

  6. If f(x) is a function satisfying f(x+a)+f(x)=0 for all x in R and pos...

    Text Solution

    |

  7. Let f(x) be a differentiable function satisfying f(x)=int(0)^(x)e^((2t...

    Text Solution

    |

  8. Ifint0^1(e^t dt)/(t+1)=a ,then find the value of int(b-1)^b(e^(-t)dt)/...

    Text Solution

    |

  9. f(x)=int1^xlogt/(1+t+t^2)dt (xge1) then prove that f(x) =f(1/x)

    Text Solution

    |

  10. f(x)=int1^x(tan^(-1)(t))/t dt \ AAx in R^+, then find the value of f...

    Text Solution

    |

  11. Evaluate: int(sqrt(2)-1)^(sqrt(2)+1)((x^2-1))/((x^2+1)^2)dx

    Text Solution

    |

  12. Evaluate: int0^(e-1)((x^2+2x-1)/2)/(x+1)dx+int1^e xlogx e^(x^(2-2)/2)d...

    Text Solution

    |

  13. Find the value of int(1/2)^(2)e^(|x-1/x|)dx.

    Text Solution

    |

  14. If I(1)=int(0)^(1)(dx)/(e^(x)(1+x)) and I(2)=int(0)^(pi//4)(e^(tan^(2)...

    Text Solution

    |

  15. If IK=int1^e(1nx)^kdx(k in I^+)dx(k in I^+), then find the value of ...

    Text Solution

    |

  16. Given Im=int1^e(logx)^mdx ,then prove that(Im)/(1-m)+m I(m-2)=e

    Text Solution

    |

  17. If I(n)=int(0)^(pi)x^(n)sinxdx, then find the value of I(5)+20I(3).

    Text Solution

    |

  18. If L(m,n)=int(0)^(1)t^(m)(1+t)^(n),dt, then prove that L(m,n)=(2^(n)...

    Text Solution

    |

  19. IfIn=int0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)In+(n-1)I(n-2...

    Text Solution

    |

  20. IfI(m , n)=int0^(pi/2)sin^m xcos^n xdx , Then show that I(m , n)=(m-1...

    Text Solution

    |