CBSE 2026 · Region 4 · Set 1 · Q33 · 5 marks
Using integration, find the area of the region enclosed by the curve $\displaystyle \mathrm{y}=|\mathrm{x}-6|$, the x -axis, and between $\displaystyle \mathrm{x}=4$ and $\displaystyle \mathrm{x}=8$.
Marking-scheme solution
Required Area $\displaystyle =\int_{4}^{8} y\, d x=\int_{4}^{8}|x-6|\, d x$
Area $\displaystyle =-\int_{4}^{6}(x-6) d x+\int_{6}^{8}(x-6) d x$
Area $\displaystyle =-\left(\dfrac{(x-6)^{2}}{2}\right)_{4}^{6}+\left(\dfrac{(x-6)^{2}}{2}\right)_{6}^{8}=2+2=4$ or $\displaystyle 4$ sq. units
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.