Question

(a) Find the coordinates of the points of intersection of y= 4/x and 2x+y=9.
Answer= (1/2,8) and (4,1) ~~I know how to get this answer~~

(b) Sketch both graphs for values of x such that x>0. ~~ Need help ~~

(c) Calculate the area between the graphs. ~~ Need help~~

Answer 1

the answer to part c is :\[\int\limits_{1/2}^{4}4/x +2x-9\]
= \[-4\ln x+x^{2}-9x\] from 1/2 to 4

Answer 2

for understanding why I used this way you can plot the graph and see the area between them...=)(I hope it be useful )

Answer 3

I should have written it this way :
\[\int\limits_{1/2}^{4}4/x - (9 - 2x)\]

Answer 4

no sorry I should have written it this way ,\[\int\limits_{1/2}^{4}-2x +9 - 4/x\]

Answer 5

15 3/4 - 12In2 is the answer. How do you use substitution in order to get to that answer?

Answer 6

ok the answer to the above integral I wrote is :\[-x ^{2 }+9x -4\ln x\]from 1/2 to 4
then We have :
\[(-4)^{2}+9(4)-4ln 4+1/4-9/2-4\ln 2\]

Answer 7

sorry \[-(4)^{2}\] is right for the first part

Answer 8

\[4\ln 4\]= \[8\ln 2\]

Answer 9

The whole answer is 15 3/4 - 12In2 ?

Answer 10

I think is 53/4 - 12ln2

Answer 11

isn't it right?

Answer 12

but why? That is the answer... yes :) but I don't know how to get it.

Answer 13

let me som min I try to explain (my problem as you've understand is my poor English=))

Answer 14

Haha, not poor english! Ok. I'll let you explain.

Answer 15

−x^2+9x−4lnx
from 1/2 to 4 then We have :
(-(4)^2+9(4)−4ln4)-(-1/4+9/2+4ln2)=
-16+36 -17/4-8ln2-4ln2 =
20-17/4 -12ln2 =
53/4-12ln2
that's all

Answer 16

Oh, Ok. Thank you!

Answer 17

Don't mention it!=)