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Example 1 Find the area enclosed by the circle x y a Solution From Fig...

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Calculus

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Example 1 Find the area enclosed by the circle x y a Solution From Fig 8 5 the whole area enclosed by the given circle 4 area of the region AOBA bounded by the curve x axis and the ordinates x 0 and x a as the circle is symmetrical about both x axis and y axis 45 ydx taking vertical strips 4 a x dx Since x y a gives As the region AOBA lies in the first quadrant y is taken as positive Integrating we get the whole area enclosed by the given circle a y 22 to be republish a x a v tu a x 0 sin 1 2 1x x0 sin 1 2 1 a sin y sin Alternatively considering horizontal strips as shown in Fig 8 6 the whole area of the region enclosed by circle X B 0 a 45 xdy 4 y dy Rationalised 2023 24 0 Why Fig 8 5 X APPLICATION OF INTEGRALS b dx A a 0 X dy O Fig 8 6 295 A a 0 ied Example 2 Find the area enclosed by the ellipse Solution From Fig 8 7 the area of the region ABA B A bounded by the ellipse area of the region AOBA in the first quadrant bounded 4 by the curve x axis and the ordinates x 0 x a as the ellipse is symmetrical about both x axis and y axis

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