Answer :

Given the boundaries of the area to be found are,


• The curve y = 4x2


• y = 0, (x-axis)


• y = 2 (a line parallel to x-axis)


• y = 4 (a line parallel to x-axis)


• The area which is occurring in the 1st quadrant is required.



As per the given boundaries,


• The curve y = 4x2, has only the positive numbers as x has even power, so it is about the y-axis equally distributed on both sides.


• y= 2 and y=4 are parallel to x-axis at of 2 and 4 units respectively from the x-axis.


As the area should be in the 1st quadrant, the four boundaries of the region to be found are,


Point A, where the curve y = 4x2 and y-axis meet i.e. A(0,4)


Point B, where the curve y = 4x2 and y=4 meet i.e. B(1,4)


Point C, where the curve y = 4x2 and y=2 meet


Point D, where the y-axis and y=2 meet i.e. D(0,2).


Consider the curve, y = 4x2


Now,



Area of the required region = Area of ABCD.




[Using the formula]



The Area of the required region


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the area of Mathematics - Board Papers

Sketch the graph Mathematics - Board Papers

Using integrationMathematics - Board Papers

Find the area of Mathematics - Board Papers