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Area Under Curves — CBSE Class 12 board PYQs

33 past board questions on Area Under Curves, arranged like the paper itself — objective first, long answers last, newest year first in each section. Open any question for its complete solution.

Multiple Choice1 Qs

Area of the region bounded by curve $y^{2} = 4 x$ and $x = 1$ is :
CBSE 2024View solution →

Long Answer32 Qs

Find the area of the region bounded by the curve $4 x^{2} + y^{2} = 36$ using integration.
CBSE 2024View solution →
Using integration, find the area of the triangle whose vertices are $(- 1, 1)$ , $(0, 5)$ and $(3, 2)$ .
CBSE 2023View solution →
Find the area bounded by the curves $y = ∣ x - 1∣$ and $y = 1$ , using integration.
CBSE 2022View solution →
Using integration, find the area of the region bounded by the triangle whose vertices are $(2, - 2)$ , $(4, 5)$ and $(6, 2)$ .
CBSE 2020View solution →
Using method of integration, find the area of the triangle whose vertices are $(1, 0)$ , $(2, 2)$ and $(3, 1)$ .
CBSE 2019View solution →
Using method of integration, find the area of the region enclosed between two circles $x^{2} + y^{2} = 4$ and $(x - 2)^{2} + y^{2} = 4$ .
CBSE 2019View solution →
Using integration, find the area of the region in the first quadrant enclosed by the x-axis, the line $y = x$ and the circle $x^{2} + y^{2} = 32$ .
CBSE 2018View solution →
Using integration, find the area of region bounded by the triangle whose vertices are $(- 2, 1)$ , $(0, 4)$ and $(2, 3)$ .
CBSE 2017View solution →
Find the area bounded by the circle $x^{2} + y^{2} = 16$ and the line $3 y = x$ in the first quadrant, using integration.
CBSE 2017View solution →
Using integration find the area of the region ${(x, y) : x^{2} + y^{2} \leq 2 a x, y^{2} \geq a x, x, y \geq 0}$ .
CBSE 2016View solution →
Using the method of integration, find the area of the triangular region whose vertices are $(2, - 2)$ , $(4, 3)$ and $(1, 2)$ .
CBSE 2016View solution →
Using integration find the area of the triangle formed by positive x-axis and tangents and normal of the circle $x^{2} + y^{2} = 4$ at $(1, 3)$ .
CBSE 2015View solution →
Using integration, find the area of the region bounded by the triangle whose vertices are $(- 1, 2)$ , $(1, 5)$ and $(3, 4)$ .
CBSE 2014View solution →
Using integration, find the area bounded by the curve $x^{2} = 4 y$ and the line $x = 4 y - 2$ .
CBSE 2013View solution →
Using integration, find the area of the region enclosed between the two circles $x^{2} + y^{2} = 4$ and $(x - 2)^{2} + y^{2} = 4$ .
CBSE 2013View solution →
Using the method of integration, find the area of the region bounded by the lines $3 x - 2 y + 1 = 0$ , $2 x + 3 y - 21 = 0$ and $x - 5 y + 9 = 0$ .
CBSE 2012View solution →
Using the method of integration, find the area of the region bounded by the following lines: $3 x - y - 3 = 0$ , $2 x + y - 12 = 0$ and $x - 2 y - 1 = 0$ .
CBSE 2012View solution →
Using the method of integration, find the area of the region bounded by the following lines: $5 x - 2 y - 10 = 0$ , $x + y - 9 = 0$ and $2 x - 5 y - 4 = 0$ .
CBSE 2012View solution →
Using integration find the area of the triangular region whose sides have equations $y = 2 x + 1$ , $y = 3 x + 1$ and $x = 4$ .
CBSE 2011View solution →
Sketch the graph of $y = ∣ x + 3∣$ and evaluate the area under the curve $y = ∣ x + 3∣$ above $x$ -axis and between $x = - 6$ to $x = 0$ .
CBSE 2011View solution →
Using integration, find the area of the enclosed region: ${(x, y) : \frac{x ^{2}}{9} + \frac{y ^{2}}{4} \leq 1 \leq \frac{x}{3} + \frac{y}{2}}$
CBSE 2010View solution →
Using integration, find the area of the enclosed region: ${(x, y) : ∣ x - 1∣ \leq y \leq 5 - x^{2}}$
CBSE 2010View solution →
Using the method of integration, find the area of the region bounded by the lines $2 x + y = 4$ , $3 x - 2 y = 6$ and $x - 3 y + 5 = 0$ .
CBSE 2009View solution →
Find the area of the region enclosed between the two circles $x^{2} + y^{2} = 9$ and $(x - 3)^{2} + y^{2} = 9$ .
CBSE 2009View solution →
Prove that the curves $y^{2} = 4 x$ and $x^{2} = 4 y$ divide the area of the square bounded by $x = 0$ , $x = 4$ , $y = 4$ and $y = 0$ into three equal parts.
CBSE 2009View solution →
Using integration, find the area of the region enclosed between the circles $x^{2} + y^{2} = 4$ and $(x - 2)^{2} + y^{2} = 4$ .
CBSE 2008View solution →
Using integration, find the area lying above x-axis and included between the circle $x^{2} + y^{2} = 8 x$ and the parabola $y^{2} = 4 x$ .
CBSE 2008View solution →
Find the area of the triangle whose vertices are $(2, 7)$ , $(1, 1)$ and $(10, 8)$ .
CBSE 2007View solution →
Using integration, find the area of the region enclosed between the circles $x^{2} + y^{2} = 1$ and $(x - 1)^{2} + y^{2} = 1$ .
CBSE 2007View solution →
Using integration, find the area of the region bounded by the parabola $y^{2} = 4 x$ and the circle $4 x^{2} + 4 y^{2} = 9$ .
CBSE 2007View solution →
Find the area of the region bounded by $y^{2} = 4 x$ , $x = 1$ , $x = 4$ and x-axis in the first quadrant.
CBSE 2006View solution →
Find the area bounded by the curve $x^{2} = 4 y$ and the straight line $4 y - 2 = x$ .
CBSE 2005View solution →