• Support PF! Buy your school textbooks, materials and every day products Here!

Area between two curves problem

  • Thread starter zeezey
  • Start date
  • #1
11
0

Homework Statement


Find the area of the indicated region.
Enclosed by y = e^x, y = 2, and the y-axis




The Attempt at a Solution



So I the area should be integral of e^x - 2 which = e^x - 2x . I'm not sure what to do with the y-axis it mentions?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31

The Attempt at a Solution



So I the area should be integral of e^x - 2 which = e^x - 2x . I'm not sure what to do with the y-axis it mentions?

Firstly where does y=ex cut the y-axis?

You should then know the area between a curve and the y-axis is given by ∫ x dy. So if y=ex, how do you put x in terms of y?
 
  • #3
11
0
umm I'm not sure you mean like dx = e^x dy ?
 
  • #4
108
0
So you have e^x-2 as the integrand, as you mentioned. The mention of the y-axis is to put a lower bound on x (in this case, evaluating your integral from a-to-b by the FTC, the lower bound, a, is x=0)...then the upper bound would be the intersection of the functions. It's always helpful to draw out what you're asked for.

I'll leave it to you to find the upper bound and then evaluate your now definite integral.
 
  • #5
11
0
So I got 4ln(4) - 4 . Is this correct?
 

Related Threads for: Area between two curves problem

  • Last Post
Replies
1
Views
825
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
471
Replies
59
Views
2K
Replies
7
Views
2K
Replies
9
Views
12K
Replies
7
Views
1K
Top