CBSE 2022 · Region 1 · Set 3 · Q13 · 4 marks
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
\[\begin{aligned}
A= & \int_{-2}^{1} x^{2} d x \\
& \left.=\frac{x^{3}}{3}\right]_{-2}^{1} \\
= & \frac{1}{3}-\left(\frac{-8}{3}\right)=3
\end{aligned}
\]
Application of IntegralsArea under Simple CurvesApplycase_studymedium
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 · asked 3×
- Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is…2026 · asked 3×
- 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…2022 · asked 3×
- Find the area of the region bounded by the curve 4 x^2+y^2=36 using integration.2024 · asked 3×
- The area of the shaded region (figure) represented by the curves y=x^2, 0 ≤ x ≤ 2 and y -axis is given by2025 · asked 3×
- Sketch the graph of y=x x and hence find the area bounded by this curve, X -axis and the ordinates x=-2 and…2024 · asked 3×
- There is a triangular park in the society. The park is divided into two sections as shown in the figure. In…2026 · asked 3×
- Using integration, find the area of the region bounded by the line y=5 x+2, the x -axis and the ordinates…2025 · asked 3×
CBSE Class 12 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.