FIND THE AREA OF THE REGION ENCLOSED BY THE GIVEN CURVES

Example 1 :

Find the area of the region described.

The region bounded by y = 4(x + 1), y = 5(x + 1) and x  =  3

Solution :

x-intercepts and y-intercepts of  y = 4(x + 1)

x-intercepts and y-intercepts of  y = 5(x + 1)

Required area :

  =  (9/2 + 3) - (1/2 - 1)

  =  (15/2) - (-1/2)

  =  (15 + 1)/2

  =  16/2

  =  8

Example 2 :

Find the area of the region in the first quadrant bounded by the line y  =  2x, the line x  =  4 the curve y  =  2/x, and the x-axis.

Solution :

  =  (1 - 0) + 2(log 4 - log 1)

  =  1 + 2 (log4 - 0) 

  =  1 + log 16

Example 3 :

Find the area of the region bounded by y  =  √(2x), y  =  2x - 2 and y  =  0.

Solution :

  =  (2√2/3) (2)^3/2 - 4 + 4

  =  8/3

So, the required area is 8/3.   

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