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# Provide a challenge! :)

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113
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Anyone got algebraic or system of equations challenge?!!

Jan 1, 2020

#1
+11725
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Anyone got algebraic or system of equations challenge?!!

Jan 1, 2020
#2
+287
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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 $$\pi$$

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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
+29257
+4

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
0

Happy New Year! Alan

Guest Jan 1, 2020
#8
+108732
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If questions are repeats they should always be linked with the original.

Thanks Alan :)

Jan 1, 2020