Finding area with Ln x (2 Viewers)

[Roy216]

Hey guys could anyone help me with a maths question?

Question:
1. Change the subject of y = ln x into x (I did this one, but its necessary for next part)
(b) Hence finding the exact area bounded by the curve y = ln x, the x axis and the lines x = 2 and x = 4 (Keep in mind you cannot integrate ln x)

 

[twinklegal19]

basically convert the integral as if you're integrating e^x (this is obvious once you draw the graph and turn it around)

anyway I see sy123 is reading this thread so I guarantee you he'll post an awesome detailed solution up soon

 

[Miss World]

bro it is not "L"n ; it is "ln" lol

 

[Sy123]

Ok, so basically since this is 2U and we are going to assume we know nothing of inverse functions, we are going to split the co-ordinate plane into four sections.
One section is a rectangle formed by 4, and ln 4 (as seen in my diagram)
The other section is the little rectange formed by 2 and ln 2
The third section is the area bounded by y=ln x, the y-axis and y=ln 4 y=ln 2
The fourth section is the area bounded by y=ln x, the x-axis and x=4, x=2

So like taking the pieces out of a puzzle, we take the whole area of the big rectangle and minus our pieces until we get what we want.

Also I was afk while viewing this lol so thats why the solution took time:

Diagram

 

[Roy216]

bro it is not "L"n ; it is "ln" lol

I know... notice the description. It was just a mistake.

 

[Roy216]

Ok, so basically since this is 2U and we are going to assume we know nothing of inverse functions, we are going to split the co-ordinate plane into four sections.
One section is a rectangle formed by 4, and ln 4 (as seen in my diagram)
The other section is the little rectange formed by 2 and ln 2
The third section is the area bounded by y=ln x, the y-axis and y=ln 4 y=ln 2
The fourth section is the area bounded by y=ln x, the x-axis and x=4, x=2

So like taking the pieces out of a puzzle, we take the whole area of the big rectangle and minus our pieces until we get what we want.

Also I was afk while viewing this lol so thats why the solution took time:

Diagram

awesome ! the diagram makes it so much easier to understand. Thanks