RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 5 of Exercise 21.1

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5

Draw a rough sketch to indicate the bounded between the curve y2 = 4x and the line x = 3. Also, find the area of this region

Given equations are:

x = 3 ...... (1)


And y2 = 4x ...... (2)


Equation (1) represents a line parallel to the y - axis at a distance of 3 units and equation (2) represents a parabola with vertex at origin and x - axis as its axis; A rough sketch is given as below: -


3.PNG


We have to find the area of shaded region.


Required area


= shaded region OBCAO


= 2 (shaded region OBCO) (as it is symmetrical about the x - axis)


(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 (0,3) and the value of y varies)


(as )



On integrating we get,




On applying the limits, we get,




Hence the area of the region bounded between the line x = 3 and the parabola y2 = 4x 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