Karnataka 2nd PUC Maths Chapter 8 Important Questions 2027: Application of Integrals

The Karnataka 2nd PUC Maths Chapter 8 Important Questions 2027 are based on Application of Integrals. The chapter focuses on finding areas under curves and areas bounded by curves and lines. Important concepts include areas related to circles, ellipses, parabolas, straight lines and trigonometric curves.

The chapter material also includes MCQs across different difficulty levels, such as Easy, Average and Difficult, along with KCET questions asked in different years. Students can use the 2nd PUC Exam Pattern to understand the question paper structure and practise these Application of Integrals Questions and Answers accordingly. 

Application of Integrals Important Questions

These 2nd PUC Application of Integrals Important Questions cover key concepts related to finding areas under curves and areas bounded by curves and lines. Students can refer to the 2nd PUC Syllabus to understand the topics included in this chapter and practise questions based on circles, ellipses, parabolas, straight lines and trigonometric curves. 

• Application of Integrals 1 Mark Questions

The source does not provide a separate 1-mark classification. The following easy MCQs are useful for quick revision.

1. Area of a Circle

The area of the region bounded by the circle x2+y2=1x^2+y^2=1 is:

(A) π sq. units
(B) 2π sq. units
(C) 3π sq. units
(D) 4π sq. units

Answer: (A) π sq. units

2. Area of an Ellipse

The area of the region bounded by

x2/25+y2/16=1x^2/25 + y^2/16 = 1

is:

(A) 20π/2 sq. units
(B) 20π sq. units
(C) 16π sq. units
(D) 25π sq. units

Answer: (B) 20π sq. units

3. Area of a Straight-Line Region

The area bounded by the lines y=mxy=mx, x=1x=1, x=2x=2, and the x-axis is 6 sq. units. The value of mm is:

(A) 1
(B) 2
(C) 3
(D) 4

Answer: (D) 4

• Application of Integrals 2 Mark Questions

The source does not divide these questions by marks. The following Average-level questions can be used for practice.

4. Area Under a Line

The area bounded by y=xy=x, the x-axis and the ordinates x=−1x=-1 and x=2x=2 is:

(A) 3/2
(B) 2
(C) 5/2
(D) 3

Answer: (C) 5/2 sq. units

5. Area Between Two Curves

The area lying between the curves y2=2xy^2=2x and y=xy=x is:

(A) 1/4 sq. units
(B) 2/3 sq. units
(C) 3/4 sq. units
(D) 1/3 sq. units

Answer: (B) 2/3 sq. units

6. Area Between a Parabola and a Line

The area bounded by the line y=3xy=3x and the curve y=x2y=x^2 is:

(A) 10 sq. units
(B) 9/2 sq. units
(C) 9 sq. units
(D) 5 sq. units

Answer: (B) 9/2 sq. units

• Application of Integrals 3/5 Mark Questions

The uploaded material does not assign 3-mark or 5-mark labels. It instead marks some questions as Difficult. These questions require more steps or calculation.

7. Area Between Two Curves

In the interval (0,π/2)(0,\pi/2), the area lying between y=tan⁡xy=\tan x, y=cot⁡xy=\cot x and the X-axis is:

(A) log 2 sq. units
(B) 2 log 2 sq. units
(C) 3 log 2 sq. units
(D) 4 log 2 sq. units

Answer: (A) log 2 sq. units

8. Area Between a Circle and a Line

The smaller area enclosed by the circle x2+y2=4x^2+y^2=4 and the line x+y=2x+y=2 is:

(A) 2(π−2) sq. units
(B) (π−2) sq. units
(C) (2π−1) sq. units
(D) 2(π+2) sq. units

Answer: (B) (π−2) 

• Area Under Curves Important Questions

For a curve y=f(x)y=f(x), the area between the curve, the X-axis and x=ax=a to x=bx=b is represented using a definite integral. When the curve is below the X-axis, the absolute value of the integral is used. If the curve lies on both sides of the X-axis, the areas are considered separately.

9. Area Under a Logarithmic Curve

The area bounded by y=log⁡xy=\log x, the x-axis and the line x=ex=e is:

(A) 1+1/e1+1/e
(B) e
(C) 1
(D) 1−1/e1-1/e

Answer: (C) 1

• Area Between Curves Questions

10. Area Between Sine and Cosine Curves

The area bounded by the Y-axis, y=cos⁡xy=\cos x and y=sin⁡xy=\sin x, for 0≤x≤π/20\leq x\leq\pi/2, is:

(A) (2+1)(\sqrt2+1) sq. units
(B) (2−1)(\sqrt2-1) sq. units
(C) (2−2)(2-\sqrt2) sq. units
(D) 2\sqrt2 sq. units

Answer: (B) (2−1)(\sqrt2-1) sq. units

• Application of Integrals Numerical Problems

Application of Integrals Numerical Problems include questions based on finding areas of different regions. Important types include areas related to circles, ellipses, straight lines, parabolas and trigonometric curves. Questions also involve finding the area between two curves or between a curve and a line.

Some important questions for practice are:

1. Find the area of the region bounded by the circle x² + y² = 1.

2. Find the area of the region bounded by the ellipse x²/25 + y²/16 = 1.

3. Find the area of the region bounded by the line y = 3x and the curve y = x².

4. Find the area of the region bounded by the parabola y² = 8x and the straight line y = 2x.

5. Find the area of the region bounded by y = sin x, the x-axis and x = 0, x = π/2.

• Application of Integrals MCQs

Application of Integrals MCQs cover different types of area-based questions. These include questions on simple curves, areas between curves, circular and elliptical regions, parabolas, logarithmic curves and trigonometric functions.

Question 1

The area of the region bounded by the circle x² + y² = 1 is:

A) π sq. units
B) 2π sq. units
C) 3π sq. units
D) 4π sq. units

Answer: A) π sq. units

Question 2

The area of the region bounded by the ellipse x²/25 + y²/16 = 1 is:

A) 10π sq. units
B) 20π sq. units
C) 16π sq. units
D) 25π sq. units

Answer: B) 20π sq. units

Question 3

The area of the region bounded by the line y = 3x and the curve y = x² is:

A) 10 sq. units
B) 9/2 sq. units
C) 9 sq. units
D) 5 sq. units

Answer: B) 9/2 sq. units

Question 4

The area of the region bounded by y² = 8x and y = 2x is:

A) 8/3 sq. units
B) 16/3 sq. units
C) 4/3 sq. units
D) 3/4 sq. units

Answer: (C) 4/3 

Question 5

The area of the region bounded by the Y-axis, y = cos x and y = sin x, for 0 ≤ x ≤ π/2, is:

A) (√2 + 1) sq. units
B) (√2 − 1) sq. units
C) (2 − √2) sq. units
D) √2 sq. units

Answer: B) (√2 − 1) sq. units

Application of Integrals Important Questions PDF

Students can use the Application of Integrals Important Questions PDF for revision and MCQ practice. It includes important area-based results and 40 questions covering circles, ellipses, parabolas, straight lines and trigonometric curves.

How to Use Karnataka 2nd PUC Maths Solutions for Application of Integrals for Exam Preparation

Properly organised preparation helps students secure maximum marks in calculus. Follow these practical steps to use the Application of Integrals Questions and Answers effectively:

• Review Core Formulas First: Revise standard integration identities and formulas before solving problems. Clear basics simplify finding limits.

• Draw Rough Sketches: Always sketch the given equations to identify the exact bounded region. Visual graphs prevent errors in setting integration limits.

• Solve Previous Papers: Practice standard Application of Integrals PYQs to identify recurring patterns. Check the Karnataka 2nd PUC Previous Year Question Paper and Karnataka 2nd PUC Mid Term Question Paper for extra revision.

• Follow the Blueprint: Check the Karnataka 2nd PUC Exam Pattern 2027 to allocate appropriate time to 1-mark, 2-mark, and 5-mark questions. Track test schedules with the Karnataka 2nd PUC Mid Term Time Table 2026.

• Write Step-by-Step Solutions: Present every step clearly, including the integral setup, limits of integration, and final unit values.

Karnataka 2nd PUC Maths Chapter 8 Important Questions 2027 focuses on Applications of Integrals and area-based problems. Practising the questions from the chapter material can help students revise areas under curves, areas between curves and standard results in a structured way.

Also Check

• Karnataka 2nd PUC Mid Term Time Table 2026

• Karnataka 2nd PUC Mid Term Question Paper