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If the units for $ x $ are feet and the units for $ a(x) $ are pounds per foot, what are the units for $ da/dx $? What units does $ \displaystyle \int^8_2 a(x) \, dx $ have?

$\frac{l b}{f t^{2}}$

$\mathrm{lb}$

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Okay, X is in feet and a sub X is in pounds per foot. So what kind of units are D A D X. Okay. So the adx means take the derivative with respect to X. Of a. So I a is in pounds per feet and you're taking its derivative with respect to feet. So then it will be in pounds per feet per feet. So it was already in pounds per foot. And then you took as derivative with respect to feet. Okay, So that will be in pounds per foot per foot per foot foot or pounds per square foot or foot square? All right then. What about the integral? Okay, so remember the integral is an area, so X. Is in feet? So feet here and why? Which is a Cybex is in pounds per feet? Pounds per foot. So let's just draw a rectangle here. If we're finding this area you would be multiplying X times Y. So it would be in pounds per foot Times feet, so it would be in pounds. Yeah, sure. The integral is in pounds. You take away the foot. Okay. But the derivative is in pounds per square foot. So you've added a foot in there? Yeah, I have

Oklahoma State University