JEE Advanced | 2014Set, Relation and FunctionHard
Question
Let f : [0, 2] → R be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1.
Let F(x) =
f(√t)dt for x ∈ [0, 2]. If F′(x) = f′(x) for all x ∈ (0, 2), then F(2) equals
Let F(x) =
f(√t)dt for x ∈ [0, 2]. If F′(x) = f′(x) for all x ∈ (0, 2), then F(2) equalsOptions
A.e2 - 1
B.e4 - 1
C.e - 1
D.e4
Solution
F′(x) = f(x).2x = f′(x)
⇒
= 2x
⇒ f(x) = kex2
Given f(0) = 1 ⇒ f(x) = ex2
So F(x) =
exdx
= ex2 - 1
So F(2) = e4 - 1
⇒
= 2x⇒ f(x) = kex2
Given f(0) = 1 ⇒ f(x) = ex2
So F(x) =
exdx = ex2 - 1
So F(2) = e4 - 1
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 a...For real numbers x and y, we write x R y ⇔ x − y + √2 is an irrational number. Then the relation R is ...Consider any set of 201 observations x1, x2,...., x200, x201. It is given that 1 2 200 201. Then the mean deviation of t...f(x) and g(x) are two differentiable functions on [0, 2] such that f″(x) - g″(x) = 0 f′(1) = 2g′...Which of the following is a singleton Set -...