✓ Board-verified
Mathematics · 2026 · 5 marks
CBSE 2026 · Region 4 · Set 2 · Q33
Using integration, find the area of the region bounded by the curve y = x | x |, x -axis, x =-2 and x =2.
Using integration, find the area of the region bounded by the curve $\displaystyle \mathrm{y}=\mathrm{x}|\mathrm{x}|, \mathrm{x}$-axis, $\displaystyle \mathrm{x}=-2$ and $\displaystyle \mathrm{x}=2$.
Marking-scheme solution
Required Area $\displaystyle =-\int_{-2}^{0} x|x| d x+\int_{0}^{2} x|x| d x$
Area $\displaystyle =\int_{-2}^{0}-x^{2} d x+\int_{0}^{2} x^{2} d x$
Area $\displaystyle =-\left(\dfrac{x^{3}}{3}\right)_{-2}^{0}+\left(\dfrac{x^{3}}{3}\right)_{0}^{2}=\dfrac{8}{3}+\dfrac{8}{3}=\dfrac{16}{3}$ or $\displaystyle \dfrac{16}{3}$ sq. units
Alternative approach: Area $\displaystyle =2 \times \int_{0}^{2} x^{2} d x$ & proceed accordinglyAll Application of Integrals questions2026 question paperNCERT solutions: Application of IntegralsPractice Application of Integrals →
More from Application of Integrals
- The area of the region enclosed between the curve y=x|x|, x -axis, x=-2 and x=2 is:2025
- Find the area of the region bounded by the lines y=4 x+5, x+y=5 and 4 y=x+5, using integration.2023
- Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its…2026
- Using integration, find the area of the smaller region enclosed by the curve 4 x^2+4 y^2=9 and the line 2 x+2 y=3. OR If the area of the region…2022
- Sketch the curve described by {(x, y): 9 x^2+16 y^2=144} and find the area of the region enclosed by it, using integration.2026
- Find the area of the region bounded by the lines x-2 y=4, x=-1, x=6 and x -axis, using integration.2024
- Using integration, find the area of the region bounded by y=m x( m>0), x=1, x=2 and the x -axis.2023
- Find the area of the region bounded by curve 4 x^2=y and the line y=8 x+12, using integration.2022
CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.