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Exercise [06.06]

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Exercise [06.06]
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Sameed Zahoor Joined: 12 Mar 2008, 10:57 Posts: 69 Location: India	Exercise [06.06] We know if $y=u_{1}v_{1}$ then $dy=u_{1}dv_{1}+v_{1}du_{1}$ . Put $u_{1}=x$ and $v_{1}=x^{n-1}$ ,then put $v_{1}=xv_{2}$ where $v_{2}=x^{n-2}$ ,then put $v_{2}=xv_{3}$ where $v_{3}=x^{n-3}$ and so on till $v_{n-1}=xv_{n}$ where $v_{n}=x^{n-n}=x^0=1$ $d(x^n)=d(xx...ntimes)=(x^{n-1} +x^{n-1} +... ntimes)dx=n(x^{n-1})dx$
02 Apr 2008, 08:41

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