Question

Calculus Help

Answer 1

sounds as tho' you need to calculate the net rate of flow. Which of the given rates should be subtracted from the other rate to obtain the net rate of flow?:

Once you have that net rate, mult. it by the elapsed time, 12 minutes. What units of measurement should your final result have?

Answer 2

E(t) - F(t) ? @mathmale

Answer 3

I just dont know how to integrate E(t)

Answer 4

It says all you have to do is set it up, so I'm guessing all you have to write down is dG/dt = E(t)-F(t), then integrate it from t=0 to t=12 using a calculator

Answer 5

E(t) wont integrate for me.

Answer 6

It won'the integrate because it can't be integrated. You have to evaluate it as a definite integral, with mumbers, as in put it in the calculator with the bounds.
Your calculator will then give you a number.

Answer 7

Ive tried that.

Answer 8

http://m.wolframalpha.com/input/?i=Integrate%5BLog%5Bt%2B7%5D%2F%28t%2B2%29%2C+%7Bt%2C+0%2C+12%7D%5D&x=0&y=0

Answer 9

Is Ln the same as Log?

Answer 10

Yes. It is. nevermind.

Answer 11

Not really, but in wolfram alpha, Log is equivalent to Ln

Answer 12

Hold, hold. ln x and log x are not the same; the base of the first is e, whereas the base of the second is 10. They are definitely related to one another through the equation\[\log x = \ln x / \ln 10\]

Answer 13

Yes, but in wolfram language, when you input Log, it assumes base e, not 10.
I know, it's weird.

Answer 14

Right, so how would I integrate E(t) equation? U substitution?

Answer 15

Experiment. Suppose you know that log 2 = 0.30103. Type log 2 into wolframalpha and determine whether or not it returns the value you expect.

Then try ln 2.

The results are not the same, are they?

Answer 16

Right.

Answer 17

The results are the same

http://m.wolframalpha.com/input/?i=Log%5Be%2C+2%5D&x=0&y=0

http://m.wolframalpha.com/input/?i=Log%5B2%5D&x=0&y=0

http://m.wolframalpha.com/input/?i=Ln%5B2%5D&x=0&y=0

Answer 18

So my original integral was right.

Answer 19

Rather than affirm that, I'll say that wolframalpha is apparently "smart enough" to know the difference between ln x and log x.

Answer 20

Okay, im still confused.

Answer 21

Here

http://m.wolframalpha.com/input/?i=Integrate%5BLn%5Bt%2B7%5D%2F%28t%2B2%29%2C+%7Bt%2C+0%2C+12%7D%5D&x=0&y=0

I used Ln instead of Log
It still gives you the same result of 4.61149

Answer 22

Sorry, arianna, for having been sidetracked by those issues regarding logs.

You could jump right into the integration, without first having subtracted E(t) from F(t), if you don't mind having to integrate both (but separately) and combining the results.

Answer 23

Would you please share your work, leading up to the integration?

Answer 24

I got f(t)'s answer to be 65.13.

Answer 25

but I cant get E(t)

Answer 26

Not so interested in answers, arianna, as I am in HOW you got them.

Looking at E(t), I suspect you'll have to do numerical integration on your calculator. Is that what you used to find the integral from 0 to 10 of F(t)?