Question

Can someone kindly check my work?

Answer 1

Questions are:

Answer 2

My answers are:

1. 1
2. pi/2
3. 0.858
4. 0.120
5. 0.281

Much thanks

If you want to see my work just let me know

Answer 3

@imqwerty Hey if you would spare some time to take a look, I would greatly appreciate it (:

Answer 4

and yeah for 1 and 2 I said finite because the limit of the integral converges, hence the numerical

Answer 5

the first three are correct

Answer 6

For the fourth one did you solve x^2 = -lnx to get the intersection point?

Answer 7

Yeah; I got 0.652 and split the integral up

Answer 8

the fourth one is correct

Answer 9

\[\Large \int_{0}^{0.652^2} (e^{-y} - \sqrt{y} )^2dy\]

Answer 10

did you get the same integral

Answer 11

\(\color{#0cbb34}{\text{Originally Posted by}}\) @imqwerty
did you get the same integral
\(\color{#0cbb34}{\text{End of Quote}}\)
for the fifth one

Answer 12

\(\large (e^{-y} - \sqrt y)\) is the side length of the square

Answer 13

Oh I instead found the volume by parts again, I got something like this:

\(\int_{0}^{0.652}\left(\sqrt{y}\right)^{2}dy+\int_{0.652}^{1}\left(e^{-y}\right)^{2}dy\)

Answer 14

if you split the square base into half you won't get two smaller squares; you'd get two rectangles

Answer 15

That's a good point

Answer 16

yup, you can correct the dimensions, and it'll essentially become the same as what i wrote
\[\large\int_{0}^{0.652} \sqrt{y} \times (e^{-y} - \sqrt{y}) + \int_{0}^{0.652} e^{-y} \times (e^{-y} - \sqrt{y})\]

Answer 17

Ah okay, I got it. Thank you so much for your help (:

I really am grateful for you taking your time to help out!!! (:

Answer 18

∫ when do u use this symbol?

Answer 19

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
∫ when do u use this symbol?
\(\color{#0cbb34}{\text{End of Quote}}\)
https://www.youtube.com/watch?v=rjLJIVoQxz4

Answer 20

\(\color{#0cbb34}{\text{Originally Posted by}}\) @justjm
Ah okay, I got it. Thank you so much for your help (:

I really am grateful for you taking your time to help out!!! (:
\(\color{#0cbb34}{\text{End of Quote}}\)
np :)