The area of the circle x2 + y2 = 16 exterior to the parabola y2 = 6x is
(A)
4 (4
3)
3
π −
(B)
4 (4
3)
3
π +
(C)
4 (8
3)
3
π −
(D)
4 (8
3)
3
π +
19 The area bounded by the y-axis, y = cos x and y = sin x when 0
2
x
π
≤
≤
 is
(A) 2 ( 2 1)
−
(B)
2
−1
(C)
2
+1
(D)
2
Summary
� The area of the region bounded by the curve y = f (x), x-axis and the lines
x = a and x = b (b > a) is given by the formula: Area
( )
b
b
a
a
ydx
f x dx
=
=
∫
∫ � The area of the region bounded by the curve x = φ (y), y-axis and the lines
y = c, y = d is given by the formula: Area
( )
d
d
c
c
xdy
y dy
=
=
φ
∫
∫ APPLICATION OF INTEGRALS         377
� The area of the region enclosed between two curves y = f (x), y = g (x) and
the lines x = a, x = b is given by the formula,
[
]
Area
( )
( )
b
a f x
g x dx
=
−
∫
, where, f (x) ≥ g (x) in [a, b]
� If f (x) ≥ g (x) in [a, c] and f (x) ≤  g (x) in [c, b], a < c < b, then
[
]
[
]
Area
( )
( )
( )
( )
c
b
a
c
f x
g x dx
g x
f x dx
=
−
+
−
∫
∫