Homework Statement
A source is transmitting a sound wave of frequency 115 Hz. A receiver detects the direct sound wave and the sound reflected from a small section of wall. Speed of sound is 345 m/s.
It also gives a diagram of sound waves leaving a source, one hitting the wall, reflecting...
Ah, I can't believe I didn't think of that! I'd tried a bunch of complicated methods, trying to use inverse substition and even writing the antiderivative in terms of a factorial and summation, but it was right in front of me the whole time... Thank you!
Homework Statement
Let I_{n} = \int_{0}^{1}x^{n}e^{-x}dx
Show that 0 < I_{n} < \frac{1}{n+1}
Homework Equations
n/a
The Attempt at a Solution
I have been trying to prove this for a long time, and so far I haven't gotten anywhere. I managed to get a reduction formula for it using...
I have considered the properties of logs and, if there were no square roots surrounding each of the ln terms, then I would have an idea of what to do. Unfortunately, there are the square roots outside of the logs so I'm still pretty lost with this integral. :-/
Homework Statement
Evaluate integral from -1 to 1 of: sqrt(ln(6-x))/(sqrt(ln(6-x))+sqrt(ln(6+x)))
Homework Equations
n/a
The Attempt at a Solution
I barely know how to approach this integral. I've been trying to figure this out for a long time now, and I feel like I haven't...