CUET · MATHS · PYQ PAPER 2025
The value of \(\int_{-1}^1\left|x^3-x\right| d x\) is
- A 0
- B \(\frac{1}{4}\)
- C \(\frac{1}{2}\)
- D 1
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\int_{-1}^1\left|x^3-x\right| d x = 2 \int_{0}^1 \left|x^3-x\right| d x\) \(= 2 \int_{0}^1 (x-x^3) d x\) \(= 2 \left[\frac{x^2}{2} - \frac{x^4}{4}\right]_{0}^1\) \(= 2 \left(\left(\frac{1}{2} - \frac{1}{4}\right) - (0)\right)\) \(= 2 \left(\frac{1}{4}\right) = \frac{1}{2}\)
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