How Do You Calculate the Area Between Curves and Lines in Calculus?

[apiwowar]

find the exact area between y=e^x, y=2, and the y axis

im not looking for a solution, just hints on how to get started.
would i just go ahead and integrate the function from 0 to 2 or would i solve the function for x and then integrate or are those 2 idea just completely wrong?

thanks

 

[Mark44]

find the exact area between y=e^x, y=2, and the y axis

im not looking for a solution, just hints on how to get started.
would i just go ahead and integrate the function from 0 to 2 or would i solve the function for x and then integrate or are those 2 idea just completely wrong?

thanks

Step 1 is to sketch the region whose area you want to find. Then find where y = e^x intersects y = 2. After you have done that, you need to find the typical area element (either horizontal or vertical) and the limits of integration (which are NOT 0 and 2). There is a bit more to this problem than simply "integrat[ing] the function from 0 to 2."

 

[dacruick]

mark is right. you are looking for an area near 1.

 

[apiwowar]

yea that makes sense now, its just been a while since I've done these