NCERT Class 12 · Ch 8 Exercise 8.1 · Q1
NCERT Class 12 Maths · Chapter 8 Applications Of Integrals · Exercise 8.1 Question 1
Find the area bounded by x²/16+y²/9=1.
💡 Concept Hints
- Sketch the region, choose a vertical or horizontal strip, and find all sign changes.
- Express its area as an integral of upper minus lower (or right minus left), splitting where necessary.
✅ Step-by-Step Solution
Final Answer: 12π square units.
- The ellipse is symmetric about both axes, with upper branch y=3√(1−x²/16).
- Its complete area is 4∫₀^4 3√(1−x²/16) dx.
- Put x=4sin θ, dx=4cos θ dθ, with θ from 0 to π/2. The area becomes 48∫₀^(π/2)cos²θ dθ.
- Using ∫₀^(π/2)cos²θ dθ=π/4 gives area 12π.
Master Chapter 8: Applications Of Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Applications Of Integrals.
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…