Applications of Integrals Class 12 Mcq Test (120801)

The area enclosed by the ellipse \(\frac{x^2}{4} + \frac{y^2}{9} = 1\) is:

a) 4π square units

b) 9π square units

c) 12π square units

d) 18π square units

The area bounded by the parabola \(y = x^2 – 2\) and the x-axis from \(x = -1\) to \(x = 3\) is:

a) 10 square units

b) 12 square units

c) 14 square units

d) 16 square units

The area between the curve \(y = x^3\) and the x-axis from \(x = -2\) to \(x = 2\) is:

a) 4 square units

b) 8 square units

c) 16 square units

d) 32 square units

The area bounded by the parabola \(y = x^2\) and the x-axis between x = 0 and x = 4 is:

a) 8 square units

b) 12 square units

c) 16 square units

d) 20 square units

The area between the parabola \(y = x^2 – 4\) and the x-axis from \(x = -2\) to \(x = 2\) is:

a) 8 square units

b) 12 square units

c) 16 square units

d) 20 square units

Which method is used to find the area under a curve that is a straight line?

a) Integration

b) Differentiation

c) Substitution

d) Approximation

The area between the curve \(y = 2x^3\) and the x-axis from \(x = -1\) to \(x = 1\) is:

a) 1 square unit

b) 2 square units

c) 3 square units

d) 4 square units

The area enclosed by the ellipse \(\frac{x^2}{16} + \frac{y^2}{9} = 1\) is:

a) 4π square units

b) 6π square units

c) 9π square units

d) 12π square units

The area under the curve \(y = \sqrt{25 - x^2}\) and above the x-axis from \(x = -5\) to \(x = 5\) is:

a) 25 square units

b) 50 square units

c) 75 square units

d) 100 square units

The area bounded by the curve \(y = \sqrt{x}\) and the x-axis from \(x = 0 \) to \(x = 9\) is:

a) 12 square units

b) 18 square units

c) 27 square units

d) 36 square units