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Substitution

Started by AM4R, Nov 08 2006 10:01 PM

8 replies to this topic

#1 AM4R

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Posted 08 November 2006 - 10:01 PM

Heres another question im stuck on!! Can anyone help?

use the subst. x=4sin t to evaluate the definite integral:

(integration sign with 2 at top of it and 0 at bottom) x+1/square root 16-x^2


i think that might be hard to read tongue.gif

Thanks
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#2 The Wedge Effect

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Posted 08 November 2006 - 10:26 PM

\begin{align*}\int_0^2{\frac{{x+1}}{{\sqrt{16 - x^2 }}}}\end{align*}

Is this the expression you mean?
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#3 AM4R

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Posted 08 November 2006 - 10:27 PM

yeah exactly blink.gif

How u do that? lol
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#4 The Wedge Effect

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Posted 08 November 2006 - 10:32 PM

LaTeX render. Makes mathematical symbols easier to display properly.
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#5 AM4R

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Posted 08 November 2006 - 10:33 PM

nice one dry.gif

So any chance with help, lol?
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#6 John

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Posted 08 November 2006 - 10:35 PM

I think, but am not 100% sure.

Would you not just Integrate the expresion as normal, then integrate what x is subsituted for, and replace x with that integral and solve?
Bebo

#7 AM4R

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Posted 08 November 2006 - 10:40 PM

yeah I thats what i thought but it says in the question to use the substitution.
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#8 The Wedge Effect

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Posted 08 November 2006 - 10:44 PM

No. You replace all values of x with that substitution then you integrate the expression after you simplify. Once you've simplified the integrated expression, evaluate the definite integral as normal.

Basically, what you are trying to do is evaluate the expression:

\begin{align*} \int_0^2{\frac{{{4sin(t)+1}}}{{\sqrt{16-(4\sin (t))^2}}}} \end{align*}
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#9 AM4R

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Posted 08 November 2006 - 10:51 PM

ahh right!!! thanks alot Wedge biggrin.gif

done it! thanks
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