RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 20 of Exercise 21.1

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20

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: -


20.png


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.


Chapter Exercises

More Exercise Questions

7

Sketch the graph of in [0,4] and determine the area of the region enclosed by the curve, the x - axis and the lines x = 0, x = 4