MHT CET · Maths · Definite Integration
\(\int_{0}^{4}|x-2| d x=\)
- A 0
- B 4
- C 8
- D 2
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\(\int_{0}^{4}|x-2| d x =\int_{0}^{2}(2-x) d x+\int_{2}^{4}(x-2) d x \)
\( =2[x]_{0}^{2}-\frac{1}{2}\left[x^{2}\right]_{0}^{2}+\frac{1}{2}\left[x^{2}\right]_{2}^{4}-2[x]_{2}^{4} \)
\( =2(2)-\frac{1}{2}(4)+\frac{1}{2}(16-4)-2(4-2) \)
\( =4-2+6-4=4\)
\( =2[x]_{0}^{2}-\frac{1}{2}\left[x^{2}\right]_{0}^{2}+\frac{1}{2}\left[x^{2}\right]_{2}^{4}-2[x]_{2}^{4} \)
\( =2(2)-\frac{1}{2}(4)+\frac{1}{2}(16-4)-2(4-2) \)
\( =4-2+6-4=4\)
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