Area under the curveHard

Question

The area bounded by the curve y = xe-x ; xy = 0 and x = c, where c is the x-coordinate of the curve′s inflection point, is -

Options

A.1- 3e-2
B.1- 2e-2
C.1- e-2
D.1

Solution

    
y′ = e-x - xe-x = e-x (1- x)
y″ = - e-x - e-x (1 - x)    ⇒ - e-x (2 - x) = 0 ⇒ x = 2
so point of inflection is x = 2
A = xe-x dx
= 1 - 3e-2

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