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301 questions found · practise this subject as a set
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| # | Question | Subject and topic | Difficulty |
|---|---|---|---|
| 81 | If F′(x) = 3x² + 2x and F(1) = 5, then F(x) equals | Mathematics/Applied Mathematics Indefinite integrals |
Hard |
| 82 | To evaluate ∫ 2x cos(x²) dx, the most useful substitution is | Mathematics/Applied Mathematics Methods of integration |
Easy |
| 83 | ∫ x eˣ dx equals | Mathematics/Applied Mathematics Methods of integration |
Easy |
| 84 | ∫ dx/[x(x + 1)] equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 85 | ∫ log x dx equals | Mathematics/Applied Mathematics Methods of integration |
Medium |
| 86 | ∫ dx/(x² − 9) equals | Mathematics/Applied Mathematics Methods of integration |
Hard |
| 87 | The value of ∫₀² x dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 88 | The value of ∫ from −1 to 1 of x³ dx is | Mathematics/Applied Mathematics Definite integrals |
Easy |
| 89 | The value of ∫₀^(π/2) cos x dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 90 | The value of ∫₀^(π/2) sin x/(sin x + cos x) dx is | Mathematics/Applied Mathematics Definite integrals |
Medium |
| 91 | The value of ∫₀¹ x(1 − x)⁴ dx is | Mathematics/Applied Mathematics Definite integrals |
Hard |
| 92 | The area bounded by the line y = x, the x-axis and the line x = 4 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |
| 93 | The area enclosed by the ellipse x²/a² + y²/b² = 1 is | Mathematics/Applied Mathematics Applications of integrals |
Easy |
| 94 | The area under y = x² from x = 0 to x = 3, above the x-axis, is | Mathematics/Applied Mathematics Applications of integrals |
Medium |
| 95 | The area of the part of the circle x² + y² = 16 lying in the first quadrant is | Mathematics/Applied Mathematics Applications of integrals |
Medium |
| 96 | The area of the region bounded by the parabola y² = 4x and the line x = 4 is | Mathematics/Applied Mathematics Applications of integrals |
Hard |
| 97 | The order of the differential equation d³y/dx³ + 2 d²y/dx² + dy/dx = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Easy |
| 98 | The degree of (d²y/dx²)² + (dy/dx)³ + y = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Easy |
| 99 | The degree of the differential equation d²y/dx² + sin(dy/dx) = 0 is | Mathematics/Applied Mathematics Differential equations: basics |
Medium |
| 100 | How many arbitrary constants appear in the general solution of a differential equation of order 3? | Mathematics/Applied Mathematics Differential equations: basics |
Medium |