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Mathematics · 2023 · 5 marks
CBSE 2023 · Region 1 · Set 1 · Q35
Find the area of the region bounded by the curves x^2=y, y=x+2 and x-axis, using integration.
Find the area of the region bounded by the curves $\displaystyle x^{2}=y, y=x+2$ and x-axis, using integration.
Marking-scheme solution
Let Correct Graph :
$\displaystyle x$ coordinates of point of intersection are $\displaystyle -1,2$
Required area $\displaystyle =\int_{-2}^{-1}(x+2) d x+\int_{-1}^{0} x^{2} d x$
$\displaystyle =\left.\frac{(x+2)^{2}}{2}\right|_{-2} ^{-1}+\left.\frac{x^{3}}{3}\right|_{-1} ^{0}$
$\displaystyle =\frac{1}{2}+\frac{1}{3}=\frac{5}{6}$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.