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

…..(ii)

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.

Required area

= (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)

(from equation(ii))

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.

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