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Anyone got algebraic or system of equations challenge?!! cool

 Jan 1, 2020
 #1
avatar+11043 
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Anyone got algebraic or system of equations challenge?!!wink

laughlaughlaugh

 Jan 1, 2020
 #2
avatar+163 
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Using numerical integration techniques, 

 

\(\int _{-2}^2\left(x^3\cos \left(\frac{x}{2}\right)+\frac{1}{2}\right)\sqrt{4-x^2}dx\) would be \(\pi\)

.
 Jan 1, 2020
 #3
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Instead of posting bullsh*t with \(\bf \pi\), demonstrate the solution...  

Guest Jan 1, 2020
 #4
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wow do you have to be so rude on new years day 

Guest Jan 1, 2020
 #6
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Sorry! Where are my manners? Happy Fucking New Year!

Guest Jan 1, 2020
 #5
avatar+28357 
+2

Split the integral into two parts, so you have int(x3cos(x/2)sqrt(4-x2))dx + (1/2)int(sqrt(4-x2))dx

 

The kernel of the first integral is odd, so when integrating from -2 to +2, the result is zero.

For the second integral make the substitution x = 2theta, say, and it is a simple matter to find the result as pi.


 

 Jan 1, 2020
 #7
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Happy New Year! Alan smiley

Guest Jan 1, 2020
 #8
avatar+106922 
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Asker guest:

 

Please reinstate the original address.

If questions are repeats they should always be linked with the original.

 

Thanks Alan :)

 Jan 1, 2020

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