Home
Class 12
MATHS
Let f:(0, oo) in R and F(x) =underset(0)...

Let `f:(0, oo) in R and F(x) =underset(0)overset(x) int f(t) dt`. If `F(x^(2))=x^(2)(1+x)` then f (4) equals

A

`5//4`

B

`7`

C

`4`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (Numerical Answer Type Questions)|16 Videos
  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise EXERCISE (Concept-based) Single Correct Answer Type Questions|10 Videos
  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 1 ) Single Correct Answer Type Questions|62 Videos
  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos
  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|18 Videos

Similar Questions

Explore conceptually related problems

Let f:(0, oo) rarr R and F(x^(2))=int_(0)^(x^(2))f(t)dt. " If "F(x^(2))=x^(2)(1+x) , then f(4) is equal to ________________

Let f : (0,oo) to R and F(x)=int_(0)^(x)t f(t)dt . If F(x^(2))=x^(4)+x^(5) , then

Knowledge Check

  • Let f:(0, oo) in R and F(x) = int_(0)^(x) f(t) dt . If F(x^(2))=x^(2)(1+x) then f (4) equals

    A
    `5//4`
    B
    7
    C
    4
    D
    2
  • Let f:(0 , oo) rarr R and F(x)= int_(0)^(x) f(t) dt . If F(x^(2)) =x^(2) (1+x) , then f(4) equals

    A
    `(5)/(4)`
    B
    7
    C
    4
    D
    2
  • Let f:(0,oo)to R and F(x)=int_(0)^(x) f(t)dt. " If " F(x^(2))=x^(2)(1+x) , then f(4) equals

    A
    `(5)/(4)`
    B
    7
    C
    4
    D
    2
  • Similar Questions

    Explore conceptually related problems

    Let f:(0,oo)rarr R and F(x)=int_(0)^(x)t.f(t)dt. If F(x^(2))=x^(4)+x^(5), then sum_(r=1)^(12)f(r^(2)) equals (A) 216(B)219 (C) 221(D)225

    Let f:(0,oo)rarr R and F(x^(3))=int_(0)^(x^(2))f(t)dt If F(x^(3))=x^(3)(x^(2)+x+1), then f(27)=

    f:(0,oo)->R and F(x)=int_(0)^(x)f(t)dtIfF(x^(2))=x^(2)(1+x),thenf(4)

    Let f:(0,oo)rarrR and F(x)=int_0^x f(t)dt . If F(x^2)=x^2(1+x) , then f(4)= (A) 5/4 (B) 7 (C) 4 (D) 2

    If int_(0)^(x^(3)(1+x))f(t)dt=x then f(2) is equal to