Year 12s: what will be the first way you research your future options? >>

Integrate e^y^2 . 2y dy

chloeaj95

Steps please

Scroll to see replies

Reply 1

chloeaj95

Original post by alow

Do you mean this?

Unparseable latex formula:

\[\int {2y \times {e^{2y}}dy} \]

If so, use integration by parts.

No the e is y^2 not 2y

I've tried integration by parts but I just go round in circles

Reply 2

alow

Original post by chloeaj95

No the e is y^2 not 2y

I've tried integration by parts but I just go round in circles

EDIT: Look at what ghostwalker said, I was being a bit blonde.

(edited 10 years ago)

Reply 3

Old_Simon

Are you sure e^y^2 can be integrated at all?

Reply 4

ghostwalker

Original post by chloeaj95

Steps please

Since you can't see it by recognition, use substitution.

Let

u=y^2

I presume it's

\displaystyle\int 2ye^{y^2}\;dy

(edited 10 years ago)

Reply 5

the bear

no if you substitute u = 2y then the integration by parts works fine...

Reply 6

ztibor

Original post by chloeaj95

Steps please

The derivative of

e^{y^2}

using the chain rule is

\displaystyle \frac{d}{dy} \left (e^{y^2} \right )=e^{y^2} \cdot 2y

Then the undetermined integral of

e^{y^2}\cdot 2y

is ...?

Generally when

\displaystyle \int f(x) dx = F(x) +C

then for composite

f[g(x)]

\displaystyle \int g'(x) \cdot f[g(x)] dx=F[g(x)] +C

Your composition is from

f(y)=e^y

and

g(y)=y^2

AS g'(y)=2y
THe type of this integral is

\displaystyle \int g'(y) \cdot f[g(y)] dy

Reply 7

interstitial

If we let

u= y^2

, then using IBS, you get

\displaystyle\int e^u \mathrm d u

(edited 10 years ago)

Reply 8

davros

Original post by chloeaj95

Steps please

Use substitution u = y^2. After a while you should be able to do this integral by recognition because it involves the exact derivative of a function.

Reply 9

davros

Original post by majmuh24

If we let

u= y^2

, then using IBS, you get

\displaystyle\int e^u \mathrm d u

I hope you mean IBP, otherwise the OP is in real trouble :biggrin:

Reply 10

james22

Why are some people saying intergration by parts? This is a simple substitution question.

Reply 11

interstitial

Original post by davros

I hope you mean IBP, otherwise the OP is in real trouble :biggrin:

I was lazy and couldn't be bothered to write the whole phrase, but that won't happen again :hat2:

Posted from TSR Mobile

Reply 12

davros

Original post by james22

Why are some people saying intergration by parts? This is a simple substitution question.

I think some people were confused by the lack of latex. It's either a straightforward substitution or recognition.

Reply 13

TenOfThem

Original post by davros

I hope you mean IBP, otherwise the OP is in real trouble :biggrin:

IBS was correct that poster used substitution not parts

Reply 14

interstitial

For anyone who needs it cleared up, I believe the OP meant

2y e^{y^2}

Posted from TSR Mobile

Reply 15

TenOfThem

Original post by james22

Why are some people saying intergration by parts? This is a simple substitution question.

Not even substitution is needed, recognition (inverse chain rule)

Reply 16

L'Evil Fish

I swear the answer is just

e^(y^2)

:emo:

Reply 17

davros

Original post by TenOfThem

IBS was correct that poster used substitution not parts

IBS = Irritable Bowel Syndrome

I've never seen it used as an abbreviation in mathematics :biggrin:

Reply 18

TenOfThem

Original post by L'Evil Fish

I swear the answer is just

e^(y^2)

:emo:

It is

Reply 19

TenOfThem

Original post by davros

IBS = Irritable Bowel Syndrome

I agree

I've never seen it used as an abbreviation in mathematics :biggrin:

Me neither but it was more correct than IB in this case

Quick Reply

Latest

Articles for you

Learning resources are no longer available on The Student Room; but here's where you can find them

Course, age and previous study

Medicine entry requirements – five key things to know

What is an LLM and how could it benefit your career?

Integrate e^y^2 . 2y dy

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you