Home
Class 12
MATHS
If int(0)^(x)f(t)dt=x+int(x)^(1)tf(t)dt,...

If `int_(0)^(x)f(t)dt=x+int_(x)^(1)tf(t)dt`, then the value of f(1) is

A

0

B

1

C

-1

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Examples|8 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise - 2.1 (Level-1)|6 Videos

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise EXERCISE - II|156 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

If k int_(0)^(1) x f (3 x) dx = int_(0)^(3) t f(t) dt then k=

For x in R, x != 0 , if y(x) is a differentiable function such that x int_(1)^(x) y(t) dt=(x+1)int_(1)^(x)ty (t) dt , then y(x) equals: (where C is a constant.)

If f(x)=int_(x)^(x+1) e^(-t^(2)) dt , then the interval in which f(x) is decreasing is

y= int_(x)^(x^(2)) sqrt(5-t^(2))dt then the value of (dy)/(dx) at x= sqrt(2) is

If I_(1)=int_(1//e)^(tanx)(t)/(1+t^(2))dtandI_(2)=int_(1//e)^(cotx)(dt)/(t(1+t^(2))) then the values of I_(1)+I_(2) is

Let f be a non - negative function on the interval [0,1] . If int_(0)^(x)sqrt(1-(f'(t)))^(2)dt=int_(0)^(x)f(t)dt,0lexle1andf(0)=0 then

If f(x)=(e^(x))/(1+e^(x)),I_(1)=int_(f(-a))^(f(a))xg{x(1-x)}dxandI_(2)=int_(f(-a))^(f(a))g{x(1-x)}dx, then the value of (I_(2))/(I_(1)) is

int_(0)^(a) (f(x)+f(-x))dx=