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In this lesson, we will learn how to calculate the area of the region enclosed by a polar curve and how to find the area of a region bounded by two polar curves.

Q1:

Find the area of the region enclosed by one petal of π = 3 ( 2 π ) c o s .

Q2:

Find the area of the region that lies inside the polar curve π = 3 π c o s but outside the polar curve π = 1 + π c o s .

Q3:

Consider the polar curve π = 1 2 + π c o s . Find the area of the region inside its larger loop but outside its smaller loop.

Q4:

Find the area of the region bounded by the polar curve π = 1 β π s i n .

Q5:

Find the area of the region below the polar axis and enclosed by π = 2 β π c o s .

Q6:

Find the area inside both π = 2 + 2 π c o s and π = 2 π s i n .

Q7:

Find the area of the region enclosed by the inner loop of π = 3 + 6 π c o s .

Q8:

Find the area of the region that lies inside the polar curve π = 1 β π s i n but outside the polar curve π = 1 .

Q9:

Find the area of the region inside both π = 3 β 2 π s i n and π = β 3 + 2 π s i n .

Q10:

Find the area of the region enclosed by π = 1 + π s i n .

Q11:

Find the area of the region inside π = 1 + π c o s and outside π = π c o s .

Q12:

Find the area of the region bounded by the polar curve π = 1 π , where π 2 β€ π β€ 2 π .

Q13:

Find the area of the region that lies inside both the polar curve π = 2 2 π 2 s i n and the polar curve π = 1 .

Q14:

Find the area enclosed by the loop of the right strophoid π = 2 π β π c o s s e c .

Q15:

Find the area of the region enclosed by the inner loop of the polar curve π = 1 + 2 π s i n .

Q16:

Find the area of the region that lies inside the circle π = 3 π s i n but outside the cardioid π = 1 + π s i n .

Q17:

Find the area of the region that lies inside the polar curve π = 4 π s i n but outside the polar curve π = 2 .

Q18:

Find the area of the region enclosed by one loop of the polar curve π = 4 π s i n .

Q19:

Find the area inside the circle π = 4 π c o s and outside the circle π = 2 .

Q20:

Find the area of the region enclosed by one loop of the polar curve π = 4 3 π c o s .

Q21:

Find the area of the region bounded by the polar curve π = π + π s i n c o s , where 0 β€ π β€ π .

Q22:

Find the area of the region common to the interior of π = 4 ( 2 π ) s i n and π = 2 .

Q23:

Find the area of the region enclosed by one petal of π = 4 ( 3 π ) c o s .

Q24:

Find the area enclosed by one loop of the rose with polar equation π = 2 π c o s .

Q25:

Find the area of the region enclosed by the polar curve π = β 1 + ( 5 π ) c o s ο¨ .

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