Revision - Applications of Integrals & Differential Equations

Grade 12 Maths Higher — Revision - Applications of Integrals & Differential Equations: 25 practice questions with instant scoring and explanations.

1. The area bounded by y = x², the x-axis, and x = 0 to x = 3 is:
2. The area between y = sin x and the x-axis from x = 0 to x = π is:
3. The area enclosed between the curves y = x² and y = x is:
4. The area of the region bounded by y² = 4x and x = 1 is:
5. The area enclosed by the circle x² + y² = a² is:
6. The area of the region bounded by y = |x|, x = -1, x = 1 and the x-axis is:
7. The order of the differential equation (d²y/dx²)³ + (dy/dx)⁴ + y = 0 is:
8. The degree of the differential equation (d²y/dx²)² + cos(dy/dx) = 0 is:
9. The general solution of dy/dx = e^(x+y) is:
10. The solution of dy/dx = (1 + y²)/(1 + x²) is:
11. The integrating factor of dy/dx + y = e^x is:
12. The integrating factor of x dy/dx + y = x² is:
13. The solution of dy/dx = y/x passing through (1, 1) is:
14. A homogeneous differential equation of the form dy/dx = f(y/x) is solved by substituting:
15. The general solution of the linear DE dy/dx + Py = Q (P, Q functions of x) is:
16. The area enclosed between y = x³, x-axis, x = -1 and x = 1 is:
17. The area bounded by y = cos x, x = 0, x = π/2 and the x-axis is:
18. The differential equation representing the family y = A·cos x + B·sin x is:
19. The solution of dy/dx = -y (with y(0) = 1) is:
20. The area enclosed by the ellipse x²/a² + y²/b² = 1 is:
21. The particular solution of dy/dx = 2xy with y(0) = 1 is:
22. The area of the region {(x, y) : y² ≤ 4x, 4x² + 4y² ≤ 9} is (approx., standard NCERT):
23. Which of these is a separable differential equation?
24. The solution of dy/dx + y·tan x = sec x is:
25. The area bounded by the parabola y² = 4ax and its latus rectum is: