Mertsj
  • Mertsj
Integral Question Using integration by parts
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

Mertsj
  • Mertsj
\[\int\limits_{?}^{?}e ^{2\theta}\sin 3\theta d \theta\]
myininaya
  • myininaya
e^(2x) sin(3x) 2e^(2x) -1/3*cos(3x) 4e^(2x) -1/9*sin(3x) ..... \[=e^{2x} \cdot \frac{-1}{3} \cos(3x)-\int\limits_{}^{}2 e^{2x} \cdot \frac{-1}{3}\cos(3x) dx\] \[=e^{2x} \cdot \frac{-1}{3} \cos(3x)-[2 e^{2x} \cdot \frac{-1}{9} \sin(3x)-\int\limits_{}^{} 4 e^{2x} \cdot \frac{-1}{9} \sin(3x) dx]\] So we have \[\int\limits_{}^{}e^{2x} \sin(3x) dx=\frac{-e^{2x}}{3} \cos(3x)+\frac{2e^{2x}}{9} \sin(3x)-\frac{4}{9}\int\limits_{}^{}e^{2x} \sin(3x) dx\]
myininaya
  • myininaya
Solve for \[\int e^{2x} \sin(3x) dx\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

myininaya
  • myininaya
\[\frac{13}{9} \int\limits_{}^{}e^{2x} \sin(3x) dx=\frac{-e^{2x}}{3} \cos(3x)+\frac{2e^{2x}}{9} \sin(3x) +C\]
myininaya
  • myininaya
You might want to check me for airthmetic errors.
Mertsj
  • Mertsj
Thank you very much, my dear. I did have the correct f and g' identified and got to the point where you said "and so we have" but I couldn't identify that as progress. Thanks again.
myininaya
  • myininaya
Np. :) I hope I put enough details as far as me showing my work. Let me know if you don't understand one of the steps.
Mertsj
  • Mertsj
I will. Hopefully I can figure out the algebra.
Mertsj
  • Mertsj
When we have: \[\int\limits_{?}^{?}2e ^{2x}(\frac{-1}{3}\cos (3x)dx)\] Why don't we just pull out the constant -2/3?
myininaya
  • myininaya
you can
Mertsj
  • Mertsj
Thanks
myininaya
  • myininaya
i was just showing how you can use a table
Mertsj
  • Mertsj
Perfect!! I got it. \[\frac{1}{13}e ^{2x}(2\sin 3x-3\cos 3x)\]
Mertsj
  • Mertsj
+C of course
myininaya
  • myininaya
nice stuff! :)
Mertsj
  • Mertsj
Yep. I never would have thought of that trick of solving for the integral after it appeared again.
myininaya
  • myininaya
That is a nice little trick that comes in handy with these trig guys!
Mertsj
  • Mertsj
Yes. I think I knew it 50 years ago but didn't remember it now.
myininaya
  • myininaya
You sound as old as amistre. hehe
Mertsj
  • Mertsj
Probably older.

Looking for something else?

Not the answer you are looking for? Search for more explanations.