Home
Class 12
MATHS
Let T >0 be a fixed real number. Suppose...

Let `T >0` be a fixed real number. Suppose `f` is continuous function such that for all `x in R ,f(x+T)=f(x)dot` If `I=int_0^Tf(x)dx ,` then the value of `int_3^(3+3T)f(2x)dx` is `3/2I` (b) `2I` (c) `3I` (d) `6I`

A

`(3)/(2)I`

B

I

C

3I

D

6I

Text Solution

Verified by Experts

The correct Answer is:
C
`int_(3)^(3+3T)f(2x)dx " put "2x =yrArr dx = (1)/(2)dy`
`:. (1)/(2)int_(6)^(6++T)f(y)dy = (6I)/(2)=3I`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let T >0 be a fixed real number. Suppose f is continuous function such that for all x in R ,f(x+T)=f(x)dot If I=int_0^Tf(x)dx , then the value of int_3^(3+3T)f(2x)dx is (a) 3/2I (b) 2I (c) 3I (d) 6I

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

A continuous real function f satisfies f(2x)=3(f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

Let f be a one-to-one continuous function such that f(2)=3a n df(5)=7.G i v e nint_2^5f(x)dx=17 , then find the value of int_3^7f^(-1)(x)dx

Let f(x) be a continuous and periodic function such that f(x)=f(x+T) for all xepsilonR,Tgt0 .If int_(-2T)^(a+5T)f(x)dx=19(ag0) and int_(0)^(T)f(x)dx=2 , then find the value of int_(0)^(a)f(x)dx .

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

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

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

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))