Application of Integrals

Q1.The area bounded by y = f(x), x-axis, x = a and x = b is:

• A∫ₐᵇ f'(x) dx
• B∫ₐᵇ f(x) dx
• C|∫ₐᵇ f(x) dx|
• Df(b) – f(a)

Q2.The area between two curves y = f(x) and y = g(x) where f(x) ≥ g(x) on [a,b] is:

• A∫ₐᵇ f(x) dx – ∫ₐᵇ g(x) dx
• B∫ₐᵇ [f(x) – g(x)] dx
• C∫ₐᵇ [f(x) + g(x)] dx
• DBoth (a) and (b)

Q3.Area using the formula ∫_c^d [x_right – x_left] dy is used when:

• AThe curves are functions of x
• BThe region is more naturally bounded by horizontal lines
• CThe functions are trigonometric
• DThe area is always negative

Q4.The area between y = tan x and x-axis on [0, π/4] is:

• Alog√2
• Blog 2
• C(1/2) log 2
• Dlog(1/√2)

Q5.The area bounded by y = √x and y = x is:

• A1/3
• B1/6
• C2/3
• D1/2