Area Under Curves

Grade 12 Maths Higher — Area Under Curves: 25 practice questions with instant scoring and explanations.

1. Area under curve y = f(x) from x=a to x=b (f≥0) is:
2. Area between curves y = f(x) and y = g(x) where f ≥ g on [a,b] is:
3. Area under y = x² from x = 0 to x = 3 is:
4. Area of region bounded by y = x and y = x² is:
5. For area between curve that crosses the x-axis, we:
6. Area of ellipse x²/a² + y²/b² = 1 is:
7. Area of region bounded by y = √x, y = 0, x = 4 is:
8. Using horizontal strips (integration with respect to y) is useful when:
9. Area of region bounded by x = y², x = 4 is:
10. Arc length of curve y = f(x) from x = a to x = b is:
11. Arc length of curve x = g(y) from y = c to y = d is:
12. Volume of solid of revolution around x-axis (disk method) is:
13. Volume of solid of revolution around y-axis (shell method) is:
14. Washer method for volume uses:
15. Volume of solid with cross-sectional area A(x) from x=a to x=b:
16. Surface area of solid of revolution around x-axis:
17. Area under y = 1/x from x = 1 to x = e is:
18. Area enclosed by parabola y = 4 - x² and x-axis is:
19. Centroid of region under y = f(x) from a to b: x-coordinate is:
20. Pappus's Theorem for volume: V = A·2πr̄ where:
21. For parametric curve x = f(t), y = g(t): Arc length is:
22. Area in polar coordinates r = f(θ) from θ = α to θ = β:
23. Area of circle with radius a in polar form:
24. For curve in polar r = 2sin(θ), area enclosed is:
25. Review question for Area Under Curves