Question

1. Consider y' = ln(2x + x^2) ; y(1) = ln 9 .
a) Using the fundamental theorem of calculus, solve the differential equation. Then find y(3) .

Answer 1

hey, how's it going?

Answer 2

hii, i am good

Answer 3

do you usually use this instead of group chat?

Answer 4

yes

Answer 5

I see, so I dont really know which fundamental theorem its talking about... arent there 2 diff ones

Answer 6

the fundamental theorem of calculus that it's referring to is basically that you can take the integral of a derivative of a function and get back the function

Answer 7

O... is that the F(b)-F(a) one?

Answer 8

oh wait, that means you just take the derivitave of ln(2x+x^2)... what does it mean "solve the differential equation"? solve for what?

Answer 9

not take the derivative

Answer 10

oh yeah, the integral xD

Answer 11

how do you take the integral of something like that...

Answer 12

factor out an x so you have ln((x)(x+2))

Answer 13

do you know how you can simplify it from there using a property of logs?

Answer 14

Ohhh, right. you can split it to lnx-ln(x+2)

Answer 15

not quite right, but almost

Answer 16

sorry, got kicked off the comp for a bit o_o. i meant lnx +ln(x+2), but im not sure you can take the integral of that

Answer 17

are you just supposed to memorize what the integral of lnx is

Answer 18

oh... i just looked it up and it turns into an integration by parts problem, so many different concepts! lol

Answer 19

i got it now, thanks!

Answer 20

ok, no problem