Need Help with Integrating (e^(-x)sin(x))? Find the Solution Here!"

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In summary, the conversation is about finding the integral of (e^(-x)sin(x)) with limits 2 and 1, using integration by parts. The attempt at a solution involved using integration by parts twice, but the person got stuck and asked for help. Another person responded, suggesting to use the same trig function or exponential for both integrations by parts. The conversation ended with the person thanking everyone for their help.
  • #1
sara_87
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Homework Statement


what is the integral of (e^(-x)sin(x)) with limits 2 and 1


Homework Equations





The Attempt at a Solution



let the integral be denoted as I
i used integration by parts twice and i got that:
I=[-e^(-x)(sin(x))] + [e^(-x)(sin(x))] + I

i'm stuck now and don't know what to do, can someone help me please.
thank you very much
 
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  • #2
That's perfectly valid, but not very interesting. I think you used the wrong 'part' for one of your integrations by parts. In udv=d(uv)-vdu, you can use either the trig function or the exponential for v. In one integration you used the exponential and in the other the trig. Use the same one for both.
 
  • #4
First off, we get:
[tex]I=-e^{-x}\sin(x)|^{x=2}_{x=1}+\int{e}^{-x}\cos(x)dx[/tex]
Continue to use e^{-x} as u' in the integration by parts formula.
 
  • #5
thanx 2 all
;) ;) ;)
 

FAQ: Need Help with Integrating (e^(-x)sin(x))? Find the Solution Here!"

What is the formula for integrating (e^(-x)sin(x))?

The formula for integrating (e^(-x)sin(x)) is ∫(e^(-x)sin(x)) dx = -1/2(e^(-x))(sin(x) + cos(x)) + C.

Why is it necessary to integrate (e^(-x)sin(x))?

Integrating (e^(-x)sin(x)) allows us to find the area under the curve of the function, which is useful in many applications such as calculating work or displacement.

What are the steps for integrating (e^(-x)sin(x))?

The steps for integrating (e^(-x)sin(x)) are: 1) Use the product rule to rewrite the function as a sum of two integrals. 2) Integrate each integral using the power rule and u-substitution. 3) Simplify the resulting expression and add the constant of integration.

What are the common mistakes made when integrating (e^(-x)sin(x))?

Common mistakes when integrating (e^(-x)sin(x)) include forgetting to use the product rule, incorrect application of the power rule, and forgetting to add the constant of integration.

Are there any special cases when integrating (e^(-x)sin(x))?

Yes, when integrating (e^(-x)sin(x)), it is important to note that the integral of e^(-x) is -e^(-x), and the integral of sin(x) is -cos(x). This means that the final answer will have a negative sign, and the signs of the sine and cosine terms will be switched.

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