Home
Class 12
MATHS
Let g(x)=int0^x f(t).dt,where f is such ...

Let `g(x)=int_0^x f(t).dt`,where f is such that `1/2<=f(t)<=1` for `t in [0,1]` and `0<=f(t)<=1/2` for `t in [1,2]`.Then g(2) satisfies the inequality

Answer

Step by step text solution for Let g(x)=int_0^x f(t).dt,where f is such that 1/2<=f(t)<=1 for t in [0,1] and 0<=f(t)<=1/2 for t in [1,2].Then g(2) satisfies the inequality by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

Let g(x) = int_(x)^(2x) f(t) dt where x gt 0 and f be continuous function and 2* f(2x)=f(x) , then

If f(x)=x+int_0^1 t(x+t) f(t)dt, then find the value of the definite integral int_0^1 f(x)dx.

Knowledge Check

  • The function f(x) =int_0^xsqrt(1-t^4) dt is such that

    A
    It is defined on the interval [-1,1]
    B
    it is an incerasing function
    C
    it is an odd function
    D
    the points (0,0) is the point of infiection

  • Let f(x) = int_2^x f(t^2-3t+2) dt then

    A
    f'(2)=0
    B
    f(-2)=0
    C
    f(2)=0
    D
    f'(2)=2

    • Similar Questions

    Explore conceptually related problems

    Let f(x)=1/x^2 int_4^x (4t^2-2f'(t))dt then find the value of 9f'(4)

    Let f(x), xge0 , be a non-negative continous function,and let F(x) = int_(0)^(x)f(t)dt, xge0 , if for some cgt0,f(x)lec F(x) for all xge0 , then show that f(x)=0 for all xge0 .

    Let f(x)=int_0^xe^t(t-1)(t-2)dt , Then f decreases in the interval

    Let f(x) be a continuous function AAx in R , except at x=0, such that int_0^a f(x)dx , ain R^+ exists. If g(x)=int_x^a(f(t))/t dt , prove that int_0^af(x)dx=int_0^ag(x)dx

    Let f(x)={(0", if"-1 le x lt 0),(1", if "x =0),(2", if "0 lt x le1):} and let F(x)= int_(-1)^(x) f(t) dt, -1 le x le 1 , then

    Let f(x)=int_(1)^(x)(3^(t))/(1+t^(2))dt , where xgt0 , Then

    Home
    Profile