Find the area bounded by the curve y = cosx, x - axis and the ordinates x = 0 and x = 2π.

Given equations are:

y = cos x …..(i)

x - axis …..(ii)

x = 0 ……(iii)

x = …..(iv)

A table for values of y = cos x is: -

A rough sketch of the curves is given below: -

We have to find the area of shaded region.

Required area

= (shaded region ABOA + shaded region BCDB + shaded region DEFD)

(the area can be found by taking a small slice in each region of width Δx, then the area of that sliced part will be yΔx as it is a rectangle and then integrating it to get the area of the whole region)

(As x is between (0,) and the value of y varies)

(as y = cos x)

On integrating we get,

On applying the limits we get

= 1 - 0 + | - 1 - 1| + 0 - ( - 1) = 4

Hence the area bounded by the curve y = cosx, x - axis and the ordinates x = 0 and x = 2π is equal to 4 square units.

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