Application of Integrals - ISC Class 12 Mathematics Questions with Answers
28 past-paper questions on Application of Integrals from ISC Class 12 Mathematics papers (2027-2017), newest first. Open one to see its answer.
- The expression for finding the area of the shaded region is: 2027 · 1 mark · MCQ
- The diagram below shows the graph of $f(x) = 2x\sqrt{a^2 - x^2}$, for $-1 \le x \le a$, where $a > 1$. The line L is the tangent… 2027 · 3 marks · Short answer
- A line with equation $y = -3x + 9$ intersects the axes at the points P and Q. A parabola of the form $y = ax^2 + c$, where… 2027 · 3 marks · Short answer
- Find the area of the region bounded by $y = \sqrt{4 - x^2}$ and $x$ axis using integration. 2026 · 4 marks · Short answer
- Find the area bounded by the curve, $y = x(4 - x)$ and the $x$-axis from $x = 0$ to $x = 5$ as shown in the figure given above… 2026 · 4 marks · Short answer
- Find the area of the region bounded by the curves $y^2 = x$ and $y^2 = 4 - 3x$. 2026 · 4 marks · Short answer
- There are two curves given in the first quadrant as: $x^2 + y^2 = \pi^2, y = \sin x$. What are the points of intersection of both… 2025 · 4 marks · Long answer
- Using integration, find the area of the region bounded by the line $x - y + 2 = 0$, the curve $x = \sqrt{y}$ and $y$-axis. 2025 · 4 marks · Short answer
- A farmer has a field bounded by three lines $x + 2y = 2$, $y - x = 1$, $2x + y = 7$. Using integration, find the area of the… 2025 · 4 marks · Short answer
- The equation $y = 4 - x^2$ represents a parabola. Make a rough sketch of the graph of the given function. Determine the area… 2025 · 4 marks · Short answer
- Find the area of the region bounded by the x-axis, part of the curve $y = 1 + \frac{8}{x^2}$, and the ordinates $x = 2$ and… 2025 · 4 marks · Short answer
- Find the area enclosed by the parabola $y^2 = x$ and the line $y = 2x$. 2025 · 4 marks · Short answer
- Sketch the region enclosed bounded by the curve, $y = x|x|$ and the ordinates $x = -1$ and $x = 1$. Evaluate… 2025 · 4 marks · Short answer
- Draw a rough sketch and find the area enclosed by the curve $y = -x^2$ and the line $x + y + 2 = 0$. 2025 · 4 marks · Long answer
- Find the area enclosed between the co-ordinate axis and the curve $y^2 = 4a(x + \lambda)$ in the second quadrant. 2025 · 4 marks · Short answer
- In a classroom, a teacher explains the properties of a particular curve by saying that this particular curve has beautiful ups… 2025 · 4 marks · Long answer
- Using integration, find the area bounded by the curve $y^2 = 4ax$ and the line $x = a$ 2024 · 4 marks · Numerical
- Using integration, find the area of the region bounded by the curve $y^2 = 4x$ and $x^2 = 4y$ 2024 · 4 marks · Numerical
- Find the area of the region bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$. 2023 · 4 marks · Numerical
- If the area is bounded by the parabola $y^2 = 16x$ and the line $y = 4mx$ is $\frac{1}{12}\text{ sq units}$, then using… 2023 · 4 marks · Numerical
- Using integration, find the area of the region bounded between the line $x = 4$ and the parabola $y^2 = 16x$. 2022 · 4 marks · Short answer
- Sketch the graph of $y = |x + 4|$. Using integration, find the area of the region bounded by the curve $y = |x + 4|$ and $x = -6$… 2021 · 4 marks · Drawing
- Draw a rough sketch of the curves $y^2 = x$ and $y^2 = 4 - 3x$ and find the area enclosed between them. 2020 · 6 marks · Drawing
- Draw a rough sketch and find the area bounded by the curve $x^2 = y$ and $x + y = 2$. 2019 · 6 marks · Drawing
- Using integration, find the area of the following region… 2018 · 6 marks · Long answer
- Sketch the graph of $y = |x + 4|$. Using integration, find the area of the region bounded by the curve $y = |x + 4|$ and $x = -6$… 2018 · 4 marks · Drawing
- Draw a rough sketch of the curve and find the area of the region bounded by curve $y^2 = 8x$ and the line $x = 2$. 2018 · 4 marks · Drawing
- Draw a rough sketch of the curve $y^2 = 4x$ and find the area of the region enclosed by the curve and the line $y = x$. 2017 · 5 marks · Short answer
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