Home
Class 12
MATHS
Let f:[0,2]->R be a function which is c...

Let `f:[0,2]->R` be a function which is continuous on [0,2] and is differentiable on (0,2) with `f(0)=1` `L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x)` . for all `x in (0,2),` then `F(2)` equals (a)`e^2-1` (b) `e^4-1` (c)`e-1` (d) `e^4`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

If f(x) is continuous on [0,2] , differentiable in (0,2) ,f(0)=2, f(2)=8 and f'(x) le 3 for all x in (0,2) , then find the value of f(1) .

Let f(x)=int_(0)^(x)(e^(t))/(t)dt(xgt0), then e^(-a)[f(x+1)-f(1+a)]=

Let f:R to R be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

if f(x) is a differential function such that f(x)=int_(0)^(x)(1+2xf(t))dt&f(1)=e , then Q. int_(0)^(1)f(x)dx=

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

Let f be a differentiable function such that f'(x) = f(x) + int_(0)^(2) f(x) dx and f(0) = (4-e^(2))/(3) . Find f(x) .

Let f(x)=int_(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interval

Let f:[0,1]rarrR be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] Which of the following is true for 0 lt x lt 1 ?

Let f: R -> R be a differentiable function such that f(0) = 0,f(pi/2)=3a n df^(prime)(0)=1. If g(x)=int_x^(pi/2)[f^(prime)(t)cos e ct-cottcos e ctf(t)]dt for x(0,pi/2], then (lim)_(x -> 0)g(x)=

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Q. int0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

    Text Solution

    |

  2. Prove that int0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2)+.... .+ 1/...

    Text Solution

    |

  3. Let f:[0,2]->R be a function which is continuous on [0,2] and is diff...

    Text Solution

    |

  4. Evaluate: int0^1(1)/((1+x^2)sqrt(1-x^2))dx

    Text Solution

    |

  5. If f(x)={(e^cosx sinx ,, |x| leq 2),(2 ,, other wise):}. Then int-2^...

    Text Solution

    |

  6. Evaluate: int0^(pi//2)1/((a^2cos^2x+b^2sin^2x)^2)dx

    Text Solution

    |

  7. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx= pi^2

    Text Solution

    |

  8. Prove that 1 lt underset(0)overset(2)int((5-x)/(9-x^(2)))dx lt 6/5

    Text Solution

    |

  9. If the difference between the roots of the equation x^2+""a x""+""1...

    Text Solution

    |

  10. If m is the least value (global minimum) and M is the greatest value (...

    Text Solution

    |

  11. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

    Text Solution

    |

  12. Show that inta^b(|x|)/x dx=|b|-|a|dot

    Text Solution

    |

  13. The value of (pi^2)/(1n3)int(7/6)^(5/6)sec(pix)dxi s

    Text Solution

    |

  14. Let: f(x)=int0^x|2t-3|dtdot Then discuss continuity and differentiabil...

    Text Solution

    |

  15. If inta^b(f(x)-3x)dx=a^2-b^2 then the value of f(pi/6) is

    Text Solution

    |

  16. L e tI1=int(pi/6)^(pi/3)(sinx)/x dx ,I2=int(pi/6)^(pi/3)sin(sinx)/(sin...

    Text Solution

    |

  17. The value of int0^1e^(x^2-x)dx is (a)<1 (b) >1 (c) > e^(-1/4) ...

    Text Solution

    |

  18. Evaluate: int0^(1)x(dx)/(sqrt(1-x^(2)))

    Text Solution

    |

  19. The value of the definite integral int(0)^(1)(1+e^(-x^(2))) dx is

    Text Solution

    |

  20. Prove that 0 lt int0^1(x^7dx)/((1+x^8)^(1/3)) lt 1/8

    Text Solution

    |