12) of the region BOB′RFSB is enclosed by the
ellipse and the lines x = 0 and x = ae Note that the area of the region BOB′RFSB
= 
20
∫ae ydx
 = 
2
2
0
2
ae
b
a
x dx
a
−
∫
= 
2
2
2
–1
0
2
sin
2
2
ae
b x
a
x
a
x
a
a


−
+




= 
2
2 2
2
–1
2
sin
2
b ae a
a e
a
e
a


−
+




= 
2
–1
1
sin
ab e
e
e


−
+




EXERCISE 8 1
1 Find the area of the region bounded by the curve y2 = x and the lines x = 1,
x = 4 and the x-axis in the first quadrant