Area of standard ellipse is given by :πab.

Required area =

∫0πasinxdx=a[−cosx]π0=a(−cosπ+cos0)=a(1+1)=2a

Required area :

= = = = == sq units

Required area

∫abexdx=[ex]ba=eb−ea

Required area :

= area of ellipse – area of right angled triangle AOB.

= ab – ab = ( - 2 ) .

Required area :

sq.units.

The area bounded by y = 2cosx , x = 0 to x =2π and the axis of x in square units is

$= = == 2

Therefore , total area from x= 0 to x = 2 is 4 X 2= 8 sq. units.

The area of the figure bounded by the curve , the x – axis and the straight line x = e is

Required area :

$= = - = 1

The area enclosed by the curve is

Required area :

$= = == =