(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Integrate: [tex]-\frac{2}{\theta} \int^{\infty}_0 y e^{-2y/\theta} dy + \frac{2}{\theta} \int^{\infty}_0 y e^{-y/\theta}dy[/tex]

2. Relevant equations

3. The attempt at a solution

Let u = y/theta; y=u*theta; dy = du*theta, which becomes

[tex]-2 \int^{\infty}_0 u \theta e^{-2u} du + 2\int^{\infty}_0 u \theta e^{-u}du[/tex]

Doing each integral seperately and then adding them up:

[tex]-2 \int^{\infty}_0 u \theta e^{-2u} du = u\theta e^{-2u} |^{\infty}_0 - 2 \theta \int^{\infty}_0 e^{-2u} du = \theta e^{-2u} |^{\infty}_0 = - \theta[/tex]

[tex]2\int^{\infty}_0 u \theta e^{-u}du = -2u \theta e^{-u}|^{\infty}_0 + 2 \theta \int^{\infty}_0 e^{-u} du =-2 \theta e^{-u} |^{\infty}_0 = 2 \theta[/tex]

When I add them up, I get theta, but the answer is supposed to be (3/2)theta. Where did I make the mistake?

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# Homework Help: Integration by Parts separately

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