- #1

Physics-UG

- 45

- 5

## Homework Statement

Evaluate ∫e

^{-θ}cos2θ dθ

## Homework Equations

Integration by parts formula

∫udv = uv -∫vdu

## The Attempt at a Solution

So in calc II we just started integration by parts and I'm doing one of the assignment problems. I know I need to do the integration by parts twice, but I've hit a loop, or so it seems, which I know isn't right. Maybe someone can see my faults?

I set:

u = cos(2θ) v = -e

^{-θ}

du = -2sin(2θ) dθ dv = e

^{-θ}dθ

So by the formula I got:

= [cos(2θ)] [-e

^{-θ}] -2∫ [-e

^{-θ}] [sin(2θ) dθ]

Here I used the second integration by parts:

u = sin2θ v = e

^{-θ}

du = 2cos(2θ) dθ dv = -e

^{-θ}dθ

Solving by the formula again:

= [sin(2θ)] [e

^{-θ}] -2∫ [e

^{-θ}] [cos(2θ) dθ]

I'm not too sure where I've made my algebraic error, or if I'm on the right track and this won't just put my into a loop giving the same equation above? First question I've posted, so hopefully it follows the format ok, if it doesn't, chime in and let me know so I can fix it properly. Thanks in advance everyone!