Applications of Integrals Class 12 Mcq Test (120801)

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

a) 6π square units

b) 9π square units

c) 12π square units

d) 16π 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

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 between the curve \(y = 3x^2\) and the x-axis from x = 0 to x = 2 is:

a) 4 square units

b) 6 square units

c) 8 square units

d) 10 square units

The area enclosed by a circle of radius 5 units is:

a) 25π square units

b) 50π square units

c) 100π square units

d) 125π 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 under the curve y = 2x + 3 from x = 0 to x = 5 is:

a) 12 square units

b) 15 square units

c) 18 square units

d) 25 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

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 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