Question

Please help, find the integral of ln(y)/y^1/2 from 4 to 9

Answer 1

@sumeer

Answer 2

I know it's integration by parts and I can do the parts u v du do well but not the second part

Answer 3

What did you choose as your u, dv, du and v?

Answer 4

U=lny dv=square root y dy dv=1/square root y dy v=2square root y

Answer 5

Du is third one my bad

Answer 6

Can you read that?

Answer 7

So something like this right?

\(\Large \int^{9}_{4} \frac{lny}{\sqrt{y}} dy \)

\(\large u= lny ~~~~~ dv =\frac{1}{\sqrt{y}} \)
\(\large du=\frac{1}{y}~~~~~ v=2\sqrt{y} \)

?

Answer 8

Yes that's what I got

Answer 9

∫lny x y^-0.5 = lny∫y^-0.5 -∫(lny' x ∫y^-0.5)

Answer 10

What?

Answer 11

Are you having trouble applying the IBP rule or just solving afterwards?

Answer 12

Solving afterwards

Answer 13

I have (lny)(2y^1/2) -integral if (2y^1/2)(1/ydy)

Answer 14

Of

Answer 15

I changed square root of y to y^1/2 so it's easier for you to see

Answer 16

Since the left side is complete, you can plug in the limits

\(\Large (2y~lny)|^{9}_{4} - 2 \int^{9}_{4} \frac{1}{\sqrt{y}} \)

On the right hand side you can simplify. Take out the 2, and you are left with \(\large \frac{\sqrt{y}}{y} \) which can be simplified with the exponent rules (:

Answer 17

I'll brb just 1 sec gotta check on food

Answer 18

alrightyy

Answer 19

Okay

Answer 20

Wait why is it 2y? Not 2 square roots of y on left side?

Answer 21

But yess, once you have that, you'll just need to plug in values, integrate the right, and you'll be done (:

\(\Large (2\sqrt{y}~lny) |^{9}_{4}-2\int^{9}_{4} \frac{1}{\sqrt{y}} \)

\(\int \frac{1}{\sqrt{y}} \) as you know from previously is \(2\sqrt{y} \)

and yes, sorry, forgot the square root there :P

Answer 22

I'll let you know what I get :)

Answer 23

6ln(9)-4ln(4)-10?

Answer 24

I feel like that last part isn't right the -10

Answer 25

Once you integrated and plugged in values you should of gotten:

\(\large 4\sqrt{y}|^{9}_{4} \)

\(\large (4\sqrt{9}-4\sqrt{4}) \)

\(\Large 4(3)-4(2)\)

So 12-8, which is 4 :P

Answer 26

I just realized I forgot about the outside the integral! Oops

Answer 27

Yes I got 4 :)

Answer 28

Thank you so much @Luigi0210

Answer 29

No problem (: