FunctionHard
Question
Let f : (0, ∞) → R and F(x) = 
f(t)dt.
If F(x2) = x2 (1 + x), then f(4) equals
f(t)dt.If F(x2) = x2 (1 + x), then f(4) equals
Options
A.5/4
B.7
C.4
D.2
Solution
Given, F(x) = f(t)dt
By Leibnitz rule, F′(x) = f(x) ......(i)
But F(x2) = x2 (1 + x) = x2 + x3
⇒ F(x) = x + x3/2
⇒ F′(x) = 1 +
⇒ f(x) = 1 +
⇒ f(4) = 1 +
⇒ f(4) = 1 +
× 2 = 4
f(t)dtBy Leibnitz rule, F′(x) = f(x) ......(i)
But F(x2) = x2 (1 + x) = x2 + x3
⇒ F(x) = x + x3/2
⇒ F′(x) = 1 +
⇒ f(x) = 1 +
⇒ f(4) = 1 +
⇒ f(4) = 1 +
× 2 = 4Create a free account to view solution
View Solution FreeMore Function Questions
If f(x) = = y, (a ≠ c), then f(y) equals to...Let f(x) = , 0 ≤ x ≤1 and g(x) = 4x (1 - x), 0 ≤ x ≤ 1, then...The function f(x) = is -...If ′f′ and ′g′ are bijective functions and gof is defined, then, gof must be:...f(x) = cos √x, correct statement is -...