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Draw a rough sketch of the curve and find the area between x - axis, the curve and the ordinates x = 0, x = π.
Given equations are:
x - axis …..(ii)
x = 0 ……(iii)
x = …..(iv)
A table for values of is: -
A rough sketch of the curves is given below: -
We have to find the area of shaded region.
= (shaded region ABCDOA)
(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)
Apply reduction formula:
On integrating we get,
On applying the limits we get
Hence the area between x - axis, the curve and the ordinates x = 0, x = π is equal to square units.