CBSE Class 12 Math 2026 All Sets Solved Paper

Question : 10 of 20

Marks: +1, -0

The area bounded by the curve y = x | x | , x-axis and the ordinates x = -1 and x = 1 is given by

Solution:

y = x \lvert x \rvert

y = \begin{cases} x^2, & x \ge 0 \\ -x^2, & x < 0 \end{cases}

Area

= 2 \int\limits_{0}^{1} x^{2} dx

= 2 \times \left[ \frac{x^{3}}{3} \right]_{0}^{1}

= \frac{2}{3}

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