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Question

The area bounded by the curves y=xex,y=xex and the line x=1 is

A
2e sq. units
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B
12e sq. units
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C
1e sq. units
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D
11e sq. units
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Solution

The correct option is A 2e sq. units
y=x ex
Let dydx=0ex+xex=0 x=1

Also, at x=1,dydx changes sign from ve to +ve.
Hence, x=1 is a point of minima.

When x, y
Also,
limxxex=limxxex
=limx1ex (Applying L'Hospital Rule)
=0

Similarly, we can draw the graph of y=x ex.



Required area
=10xex dx10xexdx
=[xex]1010ex dx[xex]10+10exdx
=e(e1)(e1(e11))
=2e sq. units.

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