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CUET · MATHS · PYQ PAPER 2025

The value of \(\int_{-1}^1\left|x^3-x\right| d x\) is

  1. A 0
  2. B \(\frac{1}{4}\)
  3. C \(\frac{1}{2}\)
  4. D 1
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{1}{2}\)

Step-by-step Solution

Detailed explanation

\(\int_{-1}^1\left|x^3-x\right| d x = 2 \int_{0}^1 \left|x^3-x\right| d x\) \(= 2 \int_{0}^1 (x-x^3) d x\) \(= 2 \left[\frac{x^2}{2} - \frac{x^4}{4}\right]_{0}^1\) \(= 2 \left(\left(\frac{1}{2} - \frac{1}{4}\right) - (0)\right)\) \(= 2 \left(\frac{1}{4}\right) = \frac{1}{2}\)