Question

evaluate this integral and ill give medal

Answer 1

wehers the promplem

Answer 2

\[\int\limits_{}^{}(y+\frac{ 1}{ y })^2dy\]

Answer 3

Before attempting to integrate, please expand (y + [1/y])^2. Then break the integral up into two parts.

Answer 4

dang your smart

Answer 5

^ actually, I meant: "break the integral up into THREE parts."

Answer 6

Practice: (a+b)^2=?

Answer 7

do i need to expand it?

Answer 8

yes, expand (y+1/y) (y+1/y)

Answer 9

y^2+2+1/y^2

Answer 10

and integrate this values right?

Answer 11

1/3(y^3)+2y-y^-1

Answer 12

+c

Answer 13

yes

Answer 14

thanks

Answer 15

do i need to expand if there's a ^2 with the equation?

Answer 16

Show by example what you mean.

Answer 17

for example if theres a given: \[\int\limits_{}^{}(a-x)^2\]

Answer 18

do i need to expand?

Answer 19

@phi do i need to expand this one?

Answer 20

or its depends on the equation? if the equation have the same variable then i will expand, if theres a constant then i will not expand?

Answer 21

it depends. for (a-x)^2 dx you don't have to.

by the chain rule
u^2 du = ⅓ u^3

if u is (a-x) then du is -dx or dx= - du
and the problem , replacing (a-x) with u and dx with -du
\[ - \int u^2 du \]

Answer 22

how can i classify if i will expand it or not?

Answer 23

of course, multiplying it out also works.

but for your original problem
u= y + 1/y
du = 1 - y^-2

and we don't have anything like du "lying around". So plan B: expand

Answer 24

\[\int\limits\limits_{}^{}(a-x)^2dx\]

Answer 25

thanks that explains alot

Answer 26

... can be integrated in more than one way: by expanding that binomial or by use of a substitution, as phi has suggested. So there's no one answer to your question.

Answer 27

** u= y + 1/y
du = (1 - y^-2) dy

du should have that factor of dy in there

Answer 28

Note that you must include "dx" in your integrand.

Answer 29

yup, i forgot to put them, BTW thanks to you guys for helping..but i cant give 2 best response ^^