Answer :

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.


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