Answer :

Given equations are :

...... (1)



x = 0 (y – axis)


x = 1 (represents a line parallel to y - axis at a distance 1 to the right)


equation (1) represents a half eclipse that is symmetrical about the x - axis and also about the y - axis with center at origin.


A rough sketch is given as below: -


11.PNG


We have to find the area of shaded region.


Required area


= (shaded region OABCO)


(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 (0,1) and the value of y varies)


(as )



Substitute


So the above equation becomes,




We know,


So the above equation becomes,




Apply reduction formula:



On integrating we get,




Undo the substituting, we get





On applying the limits we get,





Hence the area under the included between the lines x = 0 and x = 1 is equal to square units.


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 :

Draw a rough sketMathematics - Exemplar

Compute the area Mathematics - Exemplar

Using integrationMathematics - Board Papers

Find the area of Mathematics - Board Papers

Find the area of Mathematics - Exemplar

Evaluate <span laMathematics - Board Papers

The area of the rMathematics - Exemplar

Find the area bouMathematics - Exemplar