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CBSE Class 12 Math 2013 Solved Paper

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Question : 19 of 29
Marks: +1, -0
Evaluate: ∫04\int\limits_{0}^{4} |x| + |x - 2| + |x - 4| dx
Solution:  
∫04\int\limits_{0}^{4} |x| + |x - 2| + |x - 4| dx
= ∫02\int\limits_{0}^{2} f (x) dx + ∫24\int\limits_{2}^{4} f (x) dx
= ∫02\int\limits_{0}^{2} x - x + 2 - x + 4 dx + ∫24\int\limits_{2}^{4} x + x - 2 - x + 4 dx
= ∫02\int\limits_{0}^{2} 6 - x dx + ∫24\int\limits_{2}^{4} x + 2 dx
= ∣6x−x22∣02\left|6x-\frac{x^2}{2}\right|_{0}^{2} + ∣x22+2x∣04\left|\frac{x^2}{2}+2x\right|_{0}^{4}
= 12 - 2 + 8 + 8 - 2 - 4 = 20
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