CBSE 2022 · Region 4 · Set 2 · Q7 · 3 marks
Using integration, find the area of the region $\displaystyle \left\{(\mathrm{x}, \mathrm{y}): \mathrm{y}^{2} \leq \mathrm{x} \leq \mathrm{y}\right\}$.
Marking-scheme solution
Clearly \(\displaystyle x\) coordinates of point of intersection are $\displaystyle 0$, $\displaystyle 1$
Required area \(\displaystyle =\int_{0}^{1}(\sqrt{x}-x) d x\)
\[\begin{aligned}
& =\left[\frac{2 x^{\frac{3}{2}}}{3}-\frac{x^{2}}{2}\right]_{0}^{1} \\
& =\frac{1}{6}
\end{aligned}
\]
Application of IntegralsArea under Simple CurvesApplyshort_answermedium
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.