Question

What do I enter in the box?

Answer 1

anything

Answer 2

did you use integration by parts?

Answer 3

looks like you might have just simplified wrong, do you know what \[e^0\] simplifies to?

Answer 4

e^0 = 1

Answer 5

\[\huge e^{-1} = \frac{1}{e} = 0.3678794411714423 \]

Answer 6

but its \[e^{-1/8}\]

Answer 7

and the outside loses the negative

Answer 8

ooh, didn't see the 8
in that case
\[\huge e^{\frac{-1}{8}} = \frac{1}{e^{\frac{1}{8}}}\]

Answer 9

So what happens with the negative sign that was before the 4?

Answer 10

because if you see inside the parenthesis the negative side doesnt change

Answer 11

im not sure what happen to it
e^-1/8 would give you a positive value
so idk where the negative sign went beside 4

Answer 12

the negative sign got distributed inside and reversed the order of the terms inside the parentheses.

Answer 13

so e^(-1/8) became the - 1/8th root (e) on the right

Answer 14

recall that fractional exponents can be written as roots \[e^\frac{a}{b} = \sqrt[b]{e^a}\]

Answer 15

If the negative sign reversed the order of the terms inside by doesn't the negative sign turn into positive?

Answer 16

Let's fill in the missing step so that it become clear what happened, the setup that the program used is a bit confusing... I'll post below in a moment.

Answer 17

\[-4\sqrt{2 \pi} [ e^{-1/8} - e^0]\] \[= 4 \sqrt{2 \pi}[-e^{-1/8} + e^0]\] \[= 4 \sqrt{2 \pi} (e^0 - e^{-1/8})\] \[= 4 \sqrt{2 \pi}(e^0 - \frac{1}{\sqrt[8]{e}})\]

Answer 18

so in the block I should put e^0?

Answer 19

probably not, just put what e^0 equals. Above you said that e^0 = 1.

Answer 20

Well according to my calculator I know that the answer should be 1.0907657200918 but it won't take that as an answer, and I knew it wouldn't even though I did get the final answer correct using that

Answer 21

The box in question though is not the final answer box. It just wants you to type in the "scratchwork" of the calculation e^0.

Answer 22

The very bottom box the I got the correct answer by putting 1.178
The box that has an "X" next to it should be 1.0907657200918, but it won't take that as an answer. The program never allows that many decimal places

Answer 23

The box that has an X next to it should not be 1.09... it should be the value of e^0 which is 1. don't subtract the 1/root(e) thing at this stage of the problem.

Answer 24

The program wants the exact number (ex: 1.495)

Answer 25

have you tried putting exactly 1 in the box yet? just curious

Answer 26

No, you think that would work?

Answer 27

I am 99% sure that would work, because the program is not asking for the exact number yet at that stage if I'm understanding correctly.

Answer 28

Ohhhh ok so they switch the numbers around right?

Answer 29

yes, that's exactly what happened.

Answer 30

very cruel of them >:|

Answer 31

It worked! Thats what was messing me up, I didn't realize that it got switched around. Thank you so much

Answer 32

no problem, it took me a while to spit it out... and I think you explained it best. :)