Mathbee CBSE Mathbee · CBSE Class 12 Maths
CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q345 Marksellipse_area

CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 34 (Applications Of Integrals)

Use integration to find the area of \(x^2/4+y^2/3=1\) between x=−2 and x=2.
Ellipse with semiaxes 2 and √3 at the same scale on both axes.
Ellipse with semiaxes 2 and √3 at the same scale on both axes.

✅ Step-by-Step Solution

Final Answer: 2π√3 square units.
  1. The upper branch is (√3/2)√(4−x²).
  2. The enclosed area is four times its integral from 0 to 2. The quarter-circle integral of √(4−x²) equals π.
  3. Multiply to obtain 2π√3.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] The upper branch is (√3/2)√(4−x²).
  • [3 marks] The enclosed area is four times its integral from 0 to 2. The quarter-circle integral of √(4−x²) equals π.
  • [1 mark] Multiply to obtain 2π√3.

Master Chapter 8: Applications Of Integrals

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Integrals.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
If x=sin t and y=sin(pt), prove (1−x²)y″−xy′+p²y=0 on regular…
Next Question →
A uniformly random card is lost from a standard deck. Two cards…

All Questions in CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38

Related Questions in Applications Of Integrals

Class 12 Applications Of Integrals · Assertion Reason
Assertion: The area between y=sin²x and the x-axis on [0,π] is greater than that for y=sin x…
Class 12 Applications Of Integrals · Assertion Reason
Assertion: The area inside 2x²+3y²=6 is greater than the area inside x²+y²−2x+4y+4=0. Reason…
Class 12 Applications Of Integrals · Assertion Reason
Assertion: The area enclosed by x²+y²=36 equals 36π square units. Reason: A circle x²+y²=r²…
Class 12 Applications Of Integrals · Assertion Reason
Assertion: The first-quadrant region enclosed by y=x³ and y=x has area 1/4 square unit…
Class 12 Applications Of Integrals · Assertion Reason
Assertion: The region between x=y² and x=3 has area 4√3 square units. Reason: Intersections…
Class 12 Applications Of Integrals · Case Study
An external elevator has an upper-semicircular floor. Its curved boundary is the upper half…