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: -


21.PNG


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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