Area Under Curves

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

1. The area between y = f(x) and the x-axis from x = a to x = b is:
2. The area between two curves y = f(x) and y = g(x) where f(x) ≥ g(x) on [a,b] is:
3. The area bounded by y = x² and y = x from 0 to 1 is:
4. The area under y = x from 0 to 2 is:
5. The area bounded by y = e^x and the x-axis from 0 to 1 is:
6. The area between y = sin(x) and y = cos(x) from x = 0 to x = π/4 is:
7. To find the area between curves, first we must:
8. The curves y = x and y = x² intersect at:
9. The area between y = x and y = x² from x = 0 to x = 1 is:
10. The area of a region enclosed by y² = x and x = 4 is:
11. Using the disk method, volume when rotating y = √x about x-axis from 0 to 1 is:
12. For the area between y = sin(x) and x-axis from 0 to π:
13. The area bounded by x = y² and x = 4 is:
14. The area enclosed by y = x³, y = 0, x = 0, x = 2 is:
15. When f(x) < 0 on [a,b], ∫[a,b] f(x) dx represents:
16. The area under one arch of y = sin(x) from 0 to π is:
17. The area of a circle with radius r using integration is:
18. Volume of solid of revolution using washer method is:
19. The area between y = 1/x² and x-axis from 1 to ∞ is:
20. Average value of f on [a,b] is (1/(b−a))∫[a,b] f(x)dx. For f(x) = x on [0,2], it is:
21. The area between parabola y = x² and line y = 2x is:
22. Arc length of y = f(x) from a to b is given by:
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