(i)Find the area bounded by x² + y² − 2 x = 0 and y = sin 
in the upper half of the circle.
(ii)Find the area bounded by the curve y = 2x 4 – x 2 , x-axis and the two ordinates corresponding to
the minima of the function.
(iii)Find area of the curve y² = (7 − x) (5 + x) above x − axis and between the ordinates x = − 5 and x = 1.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) 
(ii) 
(iii) 9 π
Sol. (i) (x – 1) 2 + y 2 =1
Area of circle is π r 2 = π
Required area = 
= 
(ii) 
= 8x 3 – 2x. 
= 0
⇒ (4x 2 – 1) x = 0
⇒ x = – 
, 0, 
Required area = 
= 
(iii) y² = (7 − x) (5 + x) at y = 0, x = 7, –5
(x –1) 2 + y 2 = (6) 2 centre (1,0)
From the figure it is clear that area is
= 
= 
= 
= 9 π
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