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Question

Let f(x)=x25x+6 be a function xR.
On the basis of the above information, answer the following question.
The area bounded by the curve f(|x|) and xaxis, in square units is

A
293
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B
283
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C
154
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D
193
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Solution

The correct option is B 283
f(|x|)=|x|25|x|+6
The point at which y=f(x) meets the xaxis are obtained by putting y=0
Therefore,
|x|25|x|+6=0, (|x|2)(|x|3)=0
|x|=2, |x|=3 x=±2, x=±3

(2,0),(3,0),(2,0),(3,0) are points on xaxis.
Required area =220ydx=2×143=283 square units.

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