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55

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PAGE: 364SET: ExercisesPROBLEM: 55
Please look in your text book for this problem Statement

The curve is  .

Graph the curve  .

Shade the required region.

Observe the graph :

Region enclosed by the given curves is between  and .

Area enclosed by the curves  and   between  and  is 

.

The curve is .

Top half of the curve is .

Observe the graph:

Curve is symmetrical about axis,

Hence the area enclosed by the loop is twice the area of top half of the curve.

.

Assume .

.

Change of integral limits:

Lower limt: If  then .

Upper limt: If  then .

Substitute  and change of limits in .

Area of the region is sq-units.

Area of the region is  sq-units.



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