Application of Integrals in past papers.

CBSE Board Examination 2026

• Board 2026 Q10Area bounded by $y = x|x|$⁠, the $x$-axis, $x = -1$ and $x = 1$
  Area bounded by a curve and the x-axis1 mark
• Board 2026 Q38Case study: a roundabout and its pond, areas by integration
  Area of a circle by integration4 marks

CBSE Board Examination 2025

• Board 2025 Q17Area bounded by $y^2 = x$⁠, $x = 4$ and the x-axis
  Area under y² = x by integration1 mark
• Board 2025 Q31Sketch $y = |x + 3|$ and find the area between $x = -6$ and $x = 0$
  Area under y = |x + 3| by integration3 marks

CBSE Board Examination 2024

• Board 2024 Q34Area of the ellipse $\frac{x^2}{16} + \frac{y^2}{4} = 1$ between $x = -2$ and $x = 2$
  Area of part of an ellipse between two lines5 marks

CBSE Board Examination 2023

• Board 2023 Q35Area bounded by $x^2 = y$⁠, $y = x + 2$ and the $x$-axis
  Area bounded by a parabola, a line and the x-axis5 marks

CBSE Board Examination 2022 (Term 2)

• Board 2022 T2 Q11Area of $\{4x^2 + 9y^2 \le 36,\ 2x + 3y \ge 6\}$⁠, or under $x - y + 1 = 0$ from $x = -2$ to $x = 3$
  Area: ellipse and a line; under a line4 marks

CBSE Sample Paper 2026-27

• Sample 2026-27 Q34Area between the circle $y = \sqrt{4 - x^2}$ and $x + y = 2$⁠; or between $y^2 = 2x$ and $x - 2y = 0$
  Area between a curve and a line5 marks

CBSE Sample Paper 2025-26

• Sample 2025-26 Q28$\int_{-4}^{2}|x + 1|\,dx$ on the graph, or the area between $x^2 = 4y$ and $y = x$
  Area by integration: |x + 1|, parabola and line3 marks

CBSE Sample Paper 2024-25

• Sample 2024-25 Q18Area bounded by $x^2 = 4y$ and the line $y = 4$
  Area between a parabola and a line1 mark
• Sample 2024-25 Q32Area bounded by $y = 20\cos 2x$⁠, $x = \frac{\pi}{6}$⁠, $x = \frac{\pi}{3}$ and the x-axis
  Area between y = 20 cos 2x and the x-axis5 marks

CBSE Sample Paper 2023-24

• Sample 2023-24 Q32Area of $\{(x, y): 0 \le y \le x^2 + 1, 0 \le y \le x + 1, 0 \le x \le 2\}$
  Area of a region bounded by a parabola and a line5 marks

CBSE Sample Paper 2022-23

• Sample 2022-23 Q32Area of $\{(x, y): 0 \le y \le x^2, 0 \le y \le x, 0 \le x \le 2\}$
  Area of a region bounded by a parabola and lines5 marks

CBSE Sample Paper 2021-22 (Term 2)

• Sample 2021-22 T2 Q12Area enclosed by $x + y = 2$⁠, $y^2 = x$ and the $x$-axis, or of $\{0 \le y \le \sqrt3x,\ x^2 + y^2 \le 4\}$
  Area: parabola and a line; circle and a line4 marks

CBSE Sample Paper 2020-21

• Sample 2020-21 Q8Area bounded by $y = x^2$⁠, the x-axis, $x = -1$ and $x = 1$
  Area under a parabola1 mark
• Sample 2020-21 Q24Area bounded by $y^2 = 8x$ and the line $x = 2$
  Area bounded by a parabola and a line2 marks
• Sample 2020-21 Q34Area between $x^2 + y^2 = 4$⁠, $y = \sqrt3x$ and the x-axis, or the area of $x^2 + 9y^2 = 36$
  Area of a circle sector; area of an ellipse3 marks

Questions that also use Application of Integrals

Their main topic is in another chapter.

• Sample 2025-26 Q23Find $\int\frac{(x - 3)}{(x - 1)^3}e^x\,dx$⁠, or the shaded area beside $x^2 = y$
  Integral of eˣ(f + f′); area beside a parabola2 marks