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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.
Find the area of the region bounded by the curve 4x² + y² = 36 using integration.
Find the area of the smaller region bounded by the curves x²/25 + y²/16 = 1 and x/5 + y/4 = 1, using integration.
A racing track is build around an elliptical ground whose equation is given by 9x² + 16y² = 144. The width of the track is 3 m as shown below: Based on given information, answer the following questions:
Sketch the curve {(x, y) : 100x² + 25y² = 2500} and find the area of the region enclosed by it, using integration.
Sketch the curve described by {(x, y) : 9x² + 16y² = 144} and find the area of the region enclosed by it, using integration.
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