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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.
= (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.