Question

How do you integrate 5e^0.1t ?

Answer 1

Try \(\int e^{t}\;dt\)

Answer 2

Do we need to add C?

Answer 3

Always.

Try \(\int 5e^{t}\;dt\)

Answer 4

5e^t/5 + C?

Answer 5

@tkhunny Come back! :P

Answer 6

No good. First, does 5e^t/5 mean \(5e^{t/5}\;or\;\dfrac{5e^{t}}{5} = e^{t}\). Go to more effort to write clearly.

Second, \(\int 5e^{t}\;dt = 5\int e^{t}\;dt = 5e^{t} + C\)

Okay, thy, \(\int e^{5t}\;dt\)

Answer 7

I'm confused...

Answer 8

The constant out front does nothing. Just bring it along.

Answer 9

So what is the answer? I'm totally lost!

Answer 10

Do you agree with these?

\(\int e^{t}\;dt = e^{t} + C\)

\(\int 5e^{t}\;dt = 5e^{t} + C\)

Answer 11

Oh I get it now. Cheers!

Answer 12

We haven't done \(\int e^{5t}\;dt\).

Answer 13

Could you just tell me the answer because I seriously don't get it? I'll make sure to do another question after this.

Answer 14

@tkhunny

Answer 15

Nope. You have to answer my questions.

Answer 16

Because I thought it was 5 x 0.1e^0.1 + 1

Answer 17

0.5e^1.1?

Answer 18

Or is it 5/1.1 * e^0.1/1.1?

Answer 19

\(\int e^{t}\;dt = e^{t} + C\)

\(\int 5e^{t}\;dt = 5e^{t} + C\)

\(\int e^{5t}\;dt = \dfrac{1}{5}e^{5t} + C\)

\(\int 5e^{5t}\;dt = 5\left(\dfrac{1}{5}\right)e^{5t} + C = e^{5t} + C\)

Find the derivatives and prove it.

Those are all the tools you need.

\(\int 5e^{t/10}\;dt\) = ??

Answer 20

e^t/10 + C?

Answer 21

Maybe. Are you just guessing?

Answer 22

I think it is.

Answer 23

Did something happen?

Answer 24

Are you just goading me into doing it?

\(\int 5e^{t/10}\;dt = 5\int e^{t/10}\;dt = 5\left(\dfrac{e^{t/10}}{1/10}\right) + C = 50e^{t/10} + C\)

Whoops! I guess you didn't prove it.

Answer 25

Can I just come back when my mind is fresh? I'm not getting anything!

Answer 26

Try a different problem. This one has two moving parts. Get used to both individual moving parts and you'll begin to see it. Look long and hard at my four examples with all the 5's.