Q. 14.3( 4 Votes )

Find the area of the region in the first quadrant bounded by the parabola y = 4x2 and the lines x = 0, y = 1 and y = 4.

Answer :


To find the area under two or more than two curves, the first crucial step is to find the INTERSECTION POINTS of the curves.





The coordinates



y = 4x2, y = 4


4 = 4x2


x = + 1


Required Area can be calculated by breaking the problem into two parts.


I. Calculate Area under the curve A and Line C


II. Subtract the area enclosed by curve A and Line B from the above area.


Therefore, the areas are:


I. = Area enclosed by line C and curve A




II. = Area enclosed by curve A and Line B.





Now the required area under the curves:




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