
15-16 Calculus – Differentiation and Integration
=
= −
1
4
1
4
4
0
2
cos
/
t
p
Therefore, the area bounded by the given curve is 1/4 units.
Example 15.15 Find the area bounded by the cycloid x = t - sin t, y = 1 - cos t with x axis, where t
being the parameter such that 0 £ t £ 2p.
Solution: The parametric equations of the given curve are x = t - sin t, y = 1 - cos t with x-axis,
where t being the parameter such that 0 £ t £ 2p.
Now, dx = (1 - cos t) dt.
Thus, the area bounded by the given curve is
g t f t dt t t dt
t dt
( ) '( ) ( cos )( cos )
( cos )
( c
α
β
π
π
∫
= − −
∫
= −
∫
= +
1 1
1
1
0
2
2
0
2
oos cos )
cos
cos
2
0
2
0
2
0
2
2
1
1 2
2
2
3
2
t t dt
t
t dt
dt
−
∫
= +
+
−
∫
=
π
π