exercise:F985f2e86e: Difference between revisions
From Stochiki
(Created page with "<div class="d-none"><math> \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow}...") |
No edit summary |
||
| Line 32: | Line 32: | ||
\newcommand{\mathds}{\mathbb} | \newcommand{\mathds}{\mathbb} | ||
</math></div> | </math></div> | ||
<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li> | ||
Integrate <math>\int \sin^5 2x \; dx</math> by using the fact | Integrate <math>\int \sin^5 2x \; dx</math> by using the fact | ||
that the exponent of the sine is an odd | that the exponent of the sine is an odd | ||
positive integer.</li> | positive integer.</li> | ||
< | <li> | ||
Integrate <math>\int \sin^5 2x \; dx</math> by using the recursion formula given in [[guide:53e4e7085f#ex7.1.4 |Problem]].</li> | |||
Integrate <math>\int \sin^5 2x \; dx</math> by using the | <li>Show that the answers obtained in (a) and (b) differ by a constant.</li> | ||
recursion formula given in [[guide:53e4e7085f#ex7.1.4 |Problem]].</li> | |||
<li>Show that the answers obtained in | |||
differ by a constant.</li> | |||
</ul> | </ul> | ||
Latest revision as of 02:14, 24 November 2024
[math]
\newcommand{\ex}[1]{\item }
\newcommand{\sx}{\item}
\newcommand{\x}{\sx}
\newcommand{\sxlab}[1]{}
\newcommand{\xlab}{\sxlab}
\newcommand{\prov}[1] {\quad #1}
\newcommand{\provx}[1] {\quad \mbox{#1}}
\newcommand{\intext}[1]{\quad \mbox{#1} \quad}
\newcommand{\R}{\mathrm{\bf R}}
\newcommand{\Q}{\mathrm{\bf Q}}
\newcommand{\Z}{\mathrm{\bf Z}}
\newcommand{\C}{\mathrm{\bf C}}
\newcommand{\dt}{\textbf}
\newcommand{\goesto}{\rightarrow}
\newcommand{\ddxof}[1]{\frac{d #1}{d x}}
\newcommand{\ddx}{\frac{d}{dx}}
\newcommand{\ddt}{\frac{d}{dt}}
\newcommand{\dydx}{\ddxof y}
\newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}}
\newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}}
\newcommand{\dist}{\mathrm{distance}}
\newcommand{\arccot}{\mathrm{arccot\:}}
\newcommand{\arccsc}{\mathrm{arccsc\:}}
\newcommand{\arcsec}{\mathrm{arcsec\:}}
\newcommand{\arctanh}{\mathrm{arctanh\:}}
\newcommand{\arcsinh}{\mathrm{arcsinh\:}}
\newcommand{\arccosh}{\mathrm{arccosh\:}}
\newcommand{\sech}{\mathrm{sech\:}}
\newcommand{\csch}{\mathrm{csch\:}}
\newcommand{\conj}[1]{\overline{#1}}
\newcommand{\mathds}{\mathbb}
[/math]
- Integrate [math]\int \sin^5 2x \; dx[/math] by using the fact that the exponent of the sine is an odd positive integer.
- Integrate [math]\int \sin^5 2x \; dx[/math] by using the recursion formula given in Problem.
- Show that the answers obtained in (a) and (b) differ by a constant.