CUET · MATHS · PYQ PAPER 2023
The area bounded by the curve \(y=x|x|, x\)-axis and the ordinates \(x=-1\) and \(x=1\) is given by:
- A \(0\)
- B \(\frac{1}{3}\)
- C \(\frac{2}{3}\)
- D \(\frac{4}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Area \(A = \int_{-1}^{1} |x|x||\ dx\) \(A = \int_{-1}^{1} x^2\ dx\) \(A = \left[ \frac{x^3}{3} \right]_{-1}^{1}\) \(A = \frac{(1)^3}{3} - \frac{(-1)^3}{3}\) \(A = \frac{1}{3} - \left(-\frac{1}{3}\right)\) \(A = \frac{2}{3}\)
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