## anonymous 5 years ago find the area between the curves. y=log x y=x x=1 x=10

1. amistre64

yay!! an easy one :)

2. amistre64

let me draw a pic to see if we got the right interpretation

3. amistre64

4. amistre64

we integrate y=x between 1 and 10 then subtract y = log(x) between 1 and 10

5. amistre64

$\int\limits_{1}^{10} (x - \log(x)). dx$

6. amistre64

x^2 x ---- - ----- from [1,10] right? 2 log(x)

7. anonymous

yes fro [1,10] and thanks for the graph!

8. amistre64

x^2/2 = 100/2 - 1/2 = 99/2 99/2 - (10/log(10) - 1/log(1)) 99/2 - (10 - 1/0).... lol; lookslike I forgot how to int my log

9. anonymous

thank you so much!

10. amistre64

libraries closing on me so good luck with this one :)

11. anonymous

12. amistre64

in about 10 minutes maybe; if they aint answered yet... gotta move to a new location :)

13. anonymous

okay i will wait thanks!

14. amistre64

log(x) = ln(x)/ln(10) 1/ln(10) is a constant so that gets put to the side for later int(ln(x)) = x(ln(x) - 1) xlnx - x ------- from 1,10 ln(10) 99/2 - [(10- 10/ln(10)) - (-1/ln(10))] is what i get