Question

calculate \[\int {sin(2t)*e^{\frac{t}{2}}}dt\]

Answer 1

\[\int {sin(2t)*e^{\frac{t}{2}}}dt\]My prof uses something like \[cos (2t)+isin(2t)=e^{2it}\\\int{e^{2it}*e^{\frac{t}{2}}}dt\]
\[=\frac{e^{(\frac{1}{2}+2i)t}}{\frac{1}{2}+2i}\]
\[=\frac{e^{\frac{t}{2}}(cos (2t)+isin(2t)}{\frac{1}{2}+2i}\]
Does anyone give me a link to figure out what the stuff is? Please.

Answer 2

have you tried integration by parts?

Answer 3

here this might explain a few things

Answer 4

one more thing likes \[Asin u \pm Bcos u=\sqrt {A^2+B^2}sin(u \pm arctan\frac{B}{A}\]

Answer 5

from what i can tell your prof. uses the trig identities for this stuff

Answer 6

I don't really see how Euler's formula helps here as you aren't using complex variables..I would just say use integration by parts.

Answer 7

Please, explain me

Answer 8

For the last one, check out the derivation of the formula: http://www.mathsisfun.com/money/compound-interest-derivation.html

I think that textbook you're using just assumes you've come across it at an earlier point and is now recalling it.

Answer 9

thank you, I will read it. The first part I type above, I attach, please check whether my question is stupid?

Answer 10

I think you're right to question your prof's method here. This is not the way I would go about the integral. I'm still trying to decipher the work.

Answer 11

Thanks for response . just the beginning of the course. haia.....

Answer 12

Thanks for the link. It's new to me and helpful. Never took accounting before---> don't know the formulae