Using integration, find the area of the region bounded by the curve y = x|x|, x-axis, x = − 2 and x = 2.

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TextApplications of Integrals in Finding AreaArea Under a Curve Using IntegrationArea Between Two Curves Using Integration

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Using integration, find the area of the ellipse x²/16 + y²/4 = 1, included between the lines x = – 2 and x = 2.

TextApplications of Integrals in Finding AreaArea Enclosed by Ellipse Using Integration

If A₁ denotes the area of region bounded by y² = 4x, x = 1 and x-axis in the first quadrant and A₂ denotes the area of region bounded by y² = 4x, x = 4, find A₁ : A₂.

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