Application of Integrals

⭐ Important Questions

1. Find area bounded by y = x² and y = x.
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   Intersection: x² = x => x(x-1) = 0 => x=0,1\nArea = ∫_0¹ (x - x²)dx = [x²/2 - x³/3]_0¹\n= 1/2 - 1/3 = 1/6 sq units
2. Find area bounded by y² = 4x and y = 2x.
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   Intersection: 4x = 4x² => 4x(1-x)=0 => x=0,1\nPoints: (0,0), (1,2)\nArea = ∫_0¹ (2√x - 2x)dx = [4x^{3/2}/3 - x²]_0¹\n= 4/3 - 1 = 1/3 sq units