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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 1 · Set 3 · Q13
Using integration, find the area of the region enclosed by the curve y =x^2, the x -axis and the ordinates x=-2 and x=1. OR Using integration, find…
Using integration, find the area of the region enclosed by the curve $\displaystyle \mathrm{y}=x^{2}$, the $\displaystyle x$-axis and the ordinates $\displaystyle x=-2$ and $\displaystyle x=1$.
OR Using integration, find the area of the region enclosed by line $\displaystyle \mathrm{y}=\sqrt{3} x$, semi-circle $\displaystyle \mathrm{y}=\sqrt{4-x^{2}}$ and $\displaystyle x$-axis in first quadrant. CASE BASED / DATA BASED QUESTION
Marking-scheme solution
Correct figure
\[\begin{aligned}
A= & \int_{-2}^{1} x^{2} d x \\
& \left.=\frac{x^{3}}{3}\right]_{-2}^{1} \\
= & \frac{1}{3}-\left(\frac{-8}{3}\right)=3
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.