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CBSE Class 12 Math 2013 Solved Paper

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Question : 19 of 29
Marks: +1, -0
Evaluate:
4
∫
0
 |x| + |x - 2| + |x - 4| dx
Solution:  
4
∫
0
 |x| + |x - 2| + |x - 4| dx
=
2
∫
0
 f (x) dx +
4
∫
2
 f (x) dx
=
2
∫
0
 x - x + 2 - x + 4 dx +
4
∫
2
 x + x - 2 - x + 4 dx
=
2
∫
0
 6 - x dx +
4
∫
2
 x + 2 dx
= |6x−
x2
2
|02 + |
x2
2
+2x|04
= 12 - 2 + 8 + 8 - 2 - 4 = 20
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