Draw a rough sketch of the curve xy –3x – 2y – 10 = 0, x - axis and the lines x = 3, x = 4.
Given equations are:
xy –3x – 2y – 10 = 0 …..(i)
y (x - 2) = 3x + 10
x - axis …..(iii)
x = 3 ……(iv)
x = 4 …..(v)
A rough sketch of the curves is given below: -
We have to find the area of shaded region.
= (shaded region ABCDA)
(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 (3,4) and the value of y varies)
Substitute u = x−2 ⟶ dx = du
Now on integrating we get
Undo substitution, we get
On applying the limits we get
Hence the area of the region bounded by the curves, xy –3x – 2y – 10 = 0, x - axis and the lines x = 3, x = 4 is equal to square units.