Question

Need (again) to find the area between y=2.5 - x and y=1/x. I have no limits. How do I proceed? Thank you.

Answer 1

I really need to understand this.
Please help.

Answer 2

You HAVE limits, you just don't know where they are because you haven't drawn the functions to find the shape! I suggest using a graphing calculator to see what you're looking at so you can build up your intuition, since visualizing functions together is hard!

Now you can see that the functions share two points. How might you find out where these points are? I'll help you understand if you have any questions!

Answer 3

here is the graph.

Answer 4

y=2.5 - x
y=1/x
0=2.5-1/x-x

so
\[\int\limits_{.5}^{2}\left( 2.5x-1/x-x \right)dx\]

Answer 5

Great. Now just integrate those three terms, term by term. You should end up with a new function F(x) in three terms. Next, evaluate the definite integral given by zpupster by substituting the indicated limits into F(x) as follows: F(2) - F(0.5).

Answer 6

but there are only two terms...

Answer 7

What are you talking about Haleo?

Answer 8

Hmm...I get the answer to 1.273. Simply this is not for me.

Answer 9

Did you find the intercept points? I haven't verified zpupsters values

Answer 10

Those intercept points are your limits that you dont know. Once you have your intercept points, or limit values in this case, you can integrate. The are in between is the difference of the top minus the bottom wouldn't you agree?

Answer 11

Step 1: Find your intercept points.
Where does 2.5 - x = 1/x? Hint: x^2 - 2.5x + 1 = 0

Answer 12

\[(2.5-\frac{ 1 }{ x }-x) dx\]

I get when I integrate:
\[x(2.5-0.5x) - \log(x)\]

which is then
\[2.5x-0.5x ^{2}-\log(x)\]

Fill in 2 in one equation and 0.5 in another (F(b) -F(a)) ...but I don't get the right answer

Answer 13

Just to be sure you get\[\ln (x) \] correct? There is a big difference

Answer 14

Hint: The reflection of the line y = lnx across the line y = x is y = e^x