Q. 214.0( 2 Votes )

# Draw a rough sketch of the curve and find the area between x - axis, the curve and the ordinates x = 0, x = π.

Answer :

Given equations are:

…..(i)

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.

Required area

= (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)

(as )

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.

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