Application of Integrals — Class 12 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Application of Integrals" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Mathematics chapter "Application of Integrals" — 8 important questions with detailed answers for CBSE b…
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Key Questions Covered:
- Find the area enclosed by the curves y = x² and y = x.
- Find the area of the region bounded by the curve y² = 4x and the line x = 1.
- Find the area of the circle x² + y² = a² using integration.
- + 5 more questions in the full chapter
Solutions Summary:
| Question | Status |
|---|---|
| Find the area enclosed by the curves y = x² and y = x. | ✓ Solved |
| Find the area of the region bounded by the curve y² = 4x … | ✓ Solved |
| Find the area of the circle x² + y² = a² using integration. | ✓ Solved |
Showing 3 of 8 questions
Q1: Find the area enclosed by the curves y = x² and y = x.
To find the area between y = x² and y = x:
Step 1: Find points of intersection.
Set x² = x
x² - x = 0
x(x - 1) = 0
x = 0 or x = 1
Step 2: Determine which curve is above.
At x = 0.5: y = 0.5 (line) and y = 0.25 (parabola)
So y = x is above y = x²
Step 3: Set up the integral.
Area = ∫₀¹ (x - x²) dx...
Q2: Find the area of the region bounded by the curve y² = 4x and the line x = 1.
To find the area bounded by parabola y² = 4x and line x = 1:
Step 1: Identify the curve.
y² = 4x is a parabola opening rightward with vertex at origin.
Step 2: Find intersection points.
When x = 1: y² = 4(1) = 4
y = ±2
Points: (1, 2) and (1, -2)
Step 3: Set up the integral.
Using x as the variabl...
Q3: Find the area of the circle x² + y² = a² using integration.
To find the area of circle x² + y² = a²:
Step 1: Use symmetry.
The circle is symmetric about both axes.
Area = 4 × (area in first quadrant)
Step 2: Express y in terms of x.
From x² + y² = a²:
y = √(a² - x²) (taking positive value for first quadrant)
Step 3: Set up the integral for first quadrant....
Showing 3 of 8 questions. Visit the full page for complete solutions.