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# integral question - unsure of extra term

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1. Hello again,

I can't find the rule for this one, not sure why there is an extra s appearing in there. Thanks so much for the help, it is appreciated!
2. Hullo, I'm not sure what you mean, the 'extra' s is there because that's the integral, well aside the constant. Do you mean how do you do the integral? Well one way is a trig substitution as is usually the case when we have square roots and square floating about.

Edit: I'm a fool, Ben-Smith is right, that's not the integral, nearly is though.
3. (Original post by mh1985)
Hello again,

I can't find the rule for this one, not sure why there is an extra s appearing in there. Thanks so much for the help, it is appreciated!
That's simply not right, just differentiate it to see.
Also you haven't put the ds in or the +C.
4. (Original post by mh1985)
Hello again,

I can't find the rule for this one, not sure why there is an extra s appearing in there. Thanks so much for the help, it is appreciated!
(Original post by ben-smith)
That's simply not right, just differentiate it to see.
Also you haven't put the ds in or the +C.

OK sorry about that, edited the OP.
5. (Original post by mh1985)
OK sorry about that, edited the OP.
Are you familiar with hyperbolic functions?
6. (Original post by ben-smith)
Are you familiar with hyperbolic functions?
not quite 100% but I've heard of them
7. You've got the 1/2 in the wrong place. It should be:

You can see that this is right by taking the derivative. The derivative of (it's a chain rule party). The derivative of , on the other hand, is .
8. (Original post by teamnoether)
You've got the 1/2 in the wrong place. It should be:

You can see that this is right by taking the derivative. The derivative of (it's a chain rule party). The derivative of , on the other hand, is .
where does the other s come from? I doubt I would have got that without knowing the answer already. thanks for the reply btw.
9. You need to make the substitution that s = 0.1sec(u). This probably seems pulled out of thin air , but comes from the fact that you have the square root of some number squared minus a constant, all inside a square root. Because would be .

We also have , so our overall integral is

because the tangents cancel.

Is that enough to get you started? If not, let me know and I can keep going.

Edit: Sorry - that came out slightly brusque upon rereading. It should have said something more like: If not, just let me know and I would be happy to keep going.

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