Integrals

Q1.The property ∫₀ᵃ f(x) dx = ∫₀ᵃ f(a–x) dx is useful for evaluating integrals containing:

• ARational functions
• BTrigonometric functions especially on [0, π/2]
• CExponential functions
• DOnly constants

Q2.∫₀^(π) x/(1+sin x) dx equals:

• Aπ
• Bπ/2
• C2π
• D0

Q3.∫sin x dx equals:

• Acos x + C
• B–cos x + C
• Csin x + C
• D–sin x + C

Q4.∫₀¹ eˣ dx equals:

• Ae
• Be – 1
• Ce + 1
• D1 – e

Q5.∫1/√(1–x²) dx equals:

• Acos⁻¹(x) + C
• Btan⁻¹(x) + C
• Csin⁻¹(x) + C
• Dsec⁻¹(x) + C