ClearStepsCLEARSTEPS AI
Teacher Login →Student Login →

Applications of Integrals: Class 12 Maths Practice Questions

6 original exam-pattern questions with full answers, matched to the current CBSE Class 12 paper design. Attempt each question before opening the answer — or start a free 14-day trial ↓ for the full bank.

Q1MCQ1 mark

The area (in sq. units) of the region bounded by the curve y = √x and the line y = 2 is:

Diagram for question 1: Applications of Integrals
Show answer
Option (c) is correct.

Explanation: The curve y = √x intersects the line y = 2 where √x = 2, i.e., x = 4. The bounded region lies between x = 0 and x = 4, with the line y = 2 above the curve y = √x.

∴ Area = ∫₀⁴ (2 − √x) dx = [2x − (2/3)x^(3/2)]₀⁴ = [2(4) − (2/3)(4)^(3/2)] − 0 = 8 − (2/3)(8) = 8 − 16/3 = 8/3 sq. units.
Q2MCQ1 mark

The area of the region bounded by the curve y = √x and the line x = 4 (in sq. units) is:

Diagram for question 2: Applications of Integrals
Show answer
Option (B) is correct.

Explanation: The required area is bounded by y = √x, the x-axis and the line x = 4 (from x = 0 to x = 4).

∴ Area = ∫₀⁴ √x dx = ∫₀⁴ x<super>1/2</super> dx

= [x<super>3/2</super> / (3/2)]₀⁴ = (2/3)[x<super>3/2</super>]₀⁴

= (2/3)[(4)<super>3/2</super> − 0] = (2/3) × 8 = 16/3 sq. units
Q3MCQ1 mark

The area of the region bounded by the curve y = x² and the x-axis, between x = 0 and x = 3, is:

Show answer
Option (B) is correct.

Explanation: Area = ∫₀³ x² dx = [x³/3]₀³ = 27/3 − 0 = 9 sq. units.
Q4MCQ1 mark

The area (in sq. units) of the region bounded by the curve y = x² and the line y = 4 is:

Diagram for question 4: Applications of Integrals
Show answer
Option (c) is correct.

Explanation: The curve y = x² and the line y = 4 intersect where x² = 4, i.e., x = ±2.

By symmetry about the y-axis,

Area = 2∫₀² (4 − x²) dx = 2[4x − x³/3]₀² = 2[8 − 8/3] = 2 · 16/3 = 32/3 sq. units.
Q5MCQ1 mark

The area (in sq. units) of the region bounded by the circle x² + y² = 9 in the first quadrant is:

Show answer
Option (C) is correct.

Explanation: The circle x² + y² = 9 has radius 3. The area enclosed by a circle of radius r is πr². In the first quadrant, the required area is one-fourth of the total area of the circle.

∴ Area = (1/4) × π(3)² = 9π/4 sq. units
Q6MCQ1 mark

The area of the region bounded by the curve y = x² and the x-axis, between x = 0 and x = 3, is:

Show answer
Option (B) is correct.

Explanation: The required area lies above the x-axis for x ∈ [0, 3], so

Area = ∫₀³ x² dx = [x³/3]₀³ = 27/3 − 0 = 9 sq. units.

Want unlimited practice on Applications of Integrals?

The full ClearSteps bank has 6+ reviewed questions on this chapter alone — with step-wise solutions, difficulty levels, and progress tracking. Verify your WhatsApp number and your free trial starts right here.

CBSE · CLASS 12
🎟️14-day free trial · code PRAC auto-applied
Mobile Number
+91
OTP will be sent to your WhatsApp

⭐ Trusted by 12,000+ students across India

All chapters →Chapter-wise PYQ →Sample Papers →
Applications of Integrals Class 12 Maths Questions