A variable force of
4x−2
pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from
x = 1
ft to
x = 18
ft. (Round your answer to two decimal places & a medal will be given for good steps as always :-) )

Question

A variable force of
4x−2
pounds moves an object along a straight line when it is x feet from the origin. Calculate the work done in moving the object from
x = 1
ft to
x = 18
ft. (Round your answer to two decimal places & a medal will be given for good steps as always :-)  )

anonymous · Answer

Ack that's supposed to be the force being:
$$4x^{-2}$$

Sorry for any confusion this typo caused

terenzreignz · Answer

$$\int\limits_{1}^{18}4x ^{-2}dx$$

anonymous · Answer

That's it?  Hmm... I thought it would have been a far more complicated setup

terenzreignz · Answer

Actually, that's as far as I can go (besides evaluating the integral, of course)
I honestly can't explain why this is the set up T.T

anonymous · Answer

I just keep getting the integral does not converge :-/

terenzreignz · Answer

Besides, if the force wasn't variable, ie, a constant c, moved from a to b, then
$$\int\limits_{a}^{b}cdx$$
would still give the work done :)

anonymous · Answer

And yes, I'm certain that's what it says:
$$4x^{-2} lbs$$

terenzreignz · Answer

pound is a unit of force, right?

anonymous · Answer

Indeed it is.  Same as a newton in terms of what it's measuring (even though they are different values)

anonymous · Answer

I would prefer it was in metric tbh lol

terenzreignz · Answer

So, was I right? do I get the remuneration? ;)

anonymous · Answer

$$lbs \neq mass$$

anonymous · Answer

Well... It's not convergent though

anonymous · Answer

So how the hell am I supposed to get a quantified answer if it doesn't converge, very odd

anonymous · Answer

But I keep re-reading the question and that is exactly, word for word, what it says

anonymous · Answer

No instructions are forthcoming for a lack of covergence

anonymous · Answer

$$\int\limits 4/x^2 dx = -4/x+constant$$

anonymous · Answer

I'll be back to check in on this tomorrow :-)

terenzreignz · Answer

$$\int\limits_{1}^{18}4x ^{-2}dx$$
$$\int\limits_{}^{}4x ^{-2}dx = -4x ^{-1} + C$$

-4/x, evaluated from 1 to 18

-4/18 - (-4/1) =  4 - 2/9
= 34/9

terenzreignz · Answer

I don't really see what's wrong, am I missing something here?

terenzreignz · Answer

I think the answer is 34/9

anonymous · Answer

You are correct and ty for showing steps so I can follow along!  :-D

terenzreignz · Answer

Haha, thanks, and no problem :)

anonymous · Answer

Nah, you're good, this is the easy part:
$$ \int\limits_{}^{}4x ^{-2}dx = -4x ^{-1} + C $$

anonymous · Answer

-2+1 = -1