Applications Of Integrals

Given curve,

y%3D

(x%2Be)

Curve cuts

x

-axis at

(1-e%2C%200)

and y-axis at

(0%2C%201)

%5Ctherefore

Required area

%3D%5Cint%5Climits_%7B1-e%7D%5E%7B0%7D1%5Ccdot%20ln%20%5Cleft(x%2Be%5Cright)dx

%3D%5Cleft%5Bln%20%5Cleft(x%2Be%5Cright)%5Ccdot%20x%5Cright%5D_%7B1-e%7D%5E%7B0%7D-%5Cint_%7B1-e%7D%5E%7B0%7D%5Cfrac%7B1%7D%7Bx%2Be%7D%5Ccdot%20x%5C%2Cdx

%3D0-%20%5Cint%5Climits_%7B1-e%7D%5E%7B0%7D%20%5Cleft(%5Cfrac%7Bx%2Be%7D%7Bx%2Be%7D-%5Cfrac%7Be%7D%7Bx%2Be%7D%5Cright)dx

%3D-%5Cint%5Climits_%7B1-e%7D%5E%7B0%7D1%20dx%20%2B%5Cint%5Climits_%7B1-e%7D%5E%7B0%7D%5Cfrac%7Be%7D%7Bx%2Be%7Ddx

%3D%5Cleft%5B-x%5Cright%5D_%7B1-e%7D%5E%7B0%7D%2B%5Cleft%5Be%5C%2Clog%5Cleft(x%2Be%5Cright)%5Cright%5D_%7B1-e%7D%5E%7B0%7D

%3D0%2B1-e%2Be%5C%2Clog%5C%2C%20e-e%5C%2C%20log%20%5Cleft(1-e%2Be%5Cright)

%3D1-e%2Be%3D1

Chapter Questions
1 MCQs