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JEE Mains · Maths · STD 12 - 8. Application and integration
Let \(f ( x )= |x -2|\) and \(g ( x )= f ( f ( x )), x \in[0,4]\) Then \(\int \limits_{0}^{3}(g(x)-f(x)) d x\) is equal to
- A \(\frac{3}{2}\)
- B \(0\)
- C \(\frac{1}{2}\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(\int_{0}^{3} g ( x )- f ( x )=\int_{0}^{3}|| x -2|-2| d x -\int_{0}^{3}| x -2| d x\) \(=\left(\frac{1}{2} \times 2 \times 2+1+\frac{1}{2} \times 1 \times 1\right)-\left(\frac{1}{2} \times 2 \times 2+\frac{1}{2} \times 1 \times 1\right)\)…
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