MHT CET · Maths · Definite Integration
\(\int_0^1 x\left|x-\frac{1}{2}\right| \mathrm{d} x=\)
- A \(\frac{1}{2}\)
- B \(\frac{1}{12}\)
- C \(\frac{1}{8}\)
- D \(\frac{1}{16}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
\(\int_0^1 x\left|x-\frac{1}{2}\right| \mathrm{d} x = \int_0^{1/2} x\left(\frac{1}{2}-x\right) \mathrm{d} x + \int_{1/2}^1 x\left(x-\frac{1}{2}\right) \mathrm{d} x\) \(= \int_0^{1/2} \left(\frac{x}{2}-x^2\right) \mathrm{d} x + \int_{1/2}^1 \left(x^2-\frac{x}{2}\right) \mathrm{d} x\)
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