Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

I Need A Hint

INT: sqrt. tanx dx

Can anybody offer me a tip on what direction to proceed at the start from? (No complete solutions though please!)

tanx= sinx/cosx .

Integrate by substitution. Let u = sqrt(tanx).

Full solution below:

Spoiler

Just use a subsitution such as u= tanx

HanaanY

tanx= sinx/cosx .

Thats quite useless in this case.

lol I was looking at my notes and I found this :
"What is the integral of tanx dx"
=INT (Sinx/Cosx)
=-ln(cosx) +c
=ln(cosx^-1) + c
Therefore, INT Tanx = ln(secx) +c

So that's why I thought it may be of some use. My bad - thats how bad I suck at maths :frown:

:frown:

OP

I think this is too difficult for me. :frown:

:frown:

I typed the expression into Mathematica Integrator and it is an incredible large answer (Not Knogle's)

Knogle

Integrate by substitution. Let u = sqrt(tanx).

Whatever you're smoking, I'd like a go. :rolleyes:

:rolleyes:

Malik

Thats quite useless in this case.

No, it would just seem you have no idea what you're on about. :rolleyes:

:rolleyes:

The hint is all you need. HanaanY, please don't apologise - you were much, much closer than any of the others. The integral is of the form -f'(x)/f(x), which is easy enough.

OP

Yes, problem with substitution is you end up having to find dx/du of sqrt. tanx also.

I will try -f'(x)/f(x) form ideas.

Wrangler

Whatever you're smoking, I'd like a go. :rolleyes:

:rolleyes:

No, it would just seem you have no idea what you're on about. :rolleyes:

:rolleyes:

Excuse my ignorance but I still fail to see the use of tanx=sinx/cosx here?

Its the SQRT(tanx).

Am I being completely thick? I don't see how sqrt(sinx)/sqrt(cosx) is of form -f'(x)/f(x) ... :confused:

:confused:

e-unit

Its the SQRT(tanx).

Am I being completely thick? I don't see how sqrt(sinx)/sqrt(cosx) is of form -f'(x)/f(x) ... :confused:

:confused:

Neither do I.

-f'(x)/f(x)

Cos is the function, -sinx is its derivative

(for Int Tanx dx)

Here you go:
http://www.thestudentroom.co.uk/showthread.php?t=156116

If you want a hint, don't read the entire thing. :wink:

:wink:

Oh, jesus - looks like I owe a couple of you an apology. I didn't see the sqrt bit!!

Sorry fellas, my bad! :redface:

:redface:

Knogle

2u du = [(secx)²] dx
2u du = (u² + 1) dx

That's not particularly correct. :smile:

:smile:

Think again about what u actually is.

OP

Excellent dvs, thank you.

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