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Savatey [412]
3 years ago
15

How large in square meters is the land area of australia (2941526 mi 2)?

Mathematics
1 answer:
cluponka [151]3 years ago
8 0
2941526 mi^2
 The first thing you should know to solve this problem is the following conversion:
 1mi = 1609.34m
 Applying the conversion we have:
 2941526 * (1609.34 / 1) ^ 2 = 7.61848E + 12 m ^ 2
 Answer: 
 The land area of Australia in square meters is:
 7.61848E + 12 m ^ 2
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how to integrate <img src="https://tex.z-dn.net/?f=e%5E%7B2s%7D%20%2ACos%20%5Cfrac%7Bs%7D%7B4%7D" id="TexFormula1" title="e^{2s}
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\int\limits {e^{2s} cos\frac{s}{4} ds    =\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s +  sin \frac{1}{4}  s} ))

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that  f(s) =  e^{2s} cos\frac{s}{4}

Now integrating

            \int\limits {f(s)} \, ds =  \int\limits {e^{2s} cos\frac{s}{4} ds

By using integration formula

   \int\limits { e^{ax} cos b x dx = \frac{e^{ax} }{a^{2}+b^{2}  } ( a cos b x + b sin b x )

<u><em>Step(ii):-</em></u>

 \int\limits {e^{2s} cos\frac{s}{4} ds    =   \frac{e^{2s} }{(2)^{2}+(\frac{1}{4}) ^{2}  } ( 2 cos (\frac{1}{4} ) s + \frac{1}{4}  sin \frac{1}{4}  s ))  

                    = \frac{e^{2s} }{(4+\frac{1}{16})} ( 2 cos (\frac{1}{4} ) s + \frac{1}{4}  sin \frac{1}{4}  s ))

                   = \frac{e^{2s} }{(\frac{65}{16} } ( \frac{8 cos (\frac{1}{4} ) s +  sin \frac{1}{4}  s}{4}  ))

                 = 16 X\frac{e^{2s} }{65 } ( \frac{8 cos (\frac{1}{4} ) s +  sin \frac{1}{4}  s}{4}  ))

                 =\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s +  sin \frac{1}{4}  s} ))

<u><em>Final answer:-</em></u>

\int\limits {e^{2s} cos\frac{s}{4} ds    =\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s +  sin \frac{1}{4}  s} ))

6 0
3 years ago
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