## anonymous one year ago Let R be the region bounded by the curve y = ln (x), the x-axis and the line x = e. Find the area of R. I need a quick answer with minimal work shown. Thanks

1. SolomonZelman

|dw:1435595958782:dw|

2. Afrodiddle

Is there a graph you are suppose to give us?

3. anonymous

That's all the question says.

4. SolomonZelman

ok, so you have to integrate that from x=1 to x=e

5. xapproachesinfinity

6. SolomonZelman

what I drew, is the picture, and x=1 is the limit of integration, because that is where the area above the x-axis starts, and x=e is the limit of integration because your region is bounded by x=e.

7. xapproachesinfinity

the regeion is from x=1 to x=e

8. xapproachesinfinity

so do integral of lnx from 1 to e

9. SolomonZelman

$$\Large\color{slate}{\displaystyle\int\limits_{1}^{e}{\rm Ln}(x)~dx}$$ like this.

10. anonymous

So just set it up and solve it

11. SolomonZelman

yup

12. anonymous

?

13. SolomonZelman

you know the integral of ln(x) right?

14. anonymous

Yes xlnx - x

15. SolomonZelman

yup, that is right. Now you have to plug in the limits of integration.

16. SolomonZelman

$$\Large\color{slate}{\displaystyle\int\limits_{1}^{e}{\rm Ln}(x)~dx=\left(x{\rm Ln} {\tiny~}x~-~x\right)~{\Huge|}_{1}^{e}}$$

17. anonymous

Yeah I got that now thanks. How would I find the volume of the same problem on the x axis and also on the y axis?

18. SolomonZelman

Volume? Do you mean that the region we drew is rotated around some line?

19. anonymous

Yeah I got that now thanks. How would I find the volume of the same problem on the x axis and also on the y axis?

20. anonymous

Yep exactly that

21. SolomonZelman

you mean the area, not the volume? if volume, then it is 3d, and probably this R is rotated around some line y=C or x=C. if area, then what area do you exactly what to find?