Math miscellaneousHard
Question
If
ex2 (x - α)dx = 0, then
ex2 (x - α)dx = 0, thenOptions
A.1 < α < 2
B.α < 0
C.0 < α < 1
D.α = 0
Solution
If
ex2(x - α)dx = 0, then ex2.x dx = ex2 a dx
(e - 1) = αex2dx
ex2 is an increasing function 0 ≤ x ≤ 1 therefore 1≤ ex2≤ e when 0 ≤ x ≤ 1
1(1-0) ≤ex2dx ≤ e(1 - 0) ⇒ 1 ≤ ex2dx ≤ e
equation (1) and (2) . we find that L.H.S. of equation is +ve andex2dx lies between 1 & e. Therefore a is a positive real no.
α =
The denominator of equation is greater than unity and numerator lies between 0 and 1.
ex2(x - α)dx = 0, then ex2.x dx = ex2 a dx(e - 1) = αex2dxex2 is an increasing function 0 ≤ x ≤ 1 therefore 1≤ ex2≤ e when 0 ≤ x ≤ 1
1(1-0) ≤
ex2dx ≤ e(1 - 0) ⇒ 1 ≤ ex2dx ≤ eequation (1) and (2) . we find that L.H.S. of equation is +ve and
ex2dx lies between 1 & e. Therefore a is a positive real no.α =
The denominator of equation is greater than unity and numerator lies between 0 and 1.Create a free account to view solution
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