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begin mathsize 14px style integral x cubed square root of 4 minus 2 x squared end root space d x equals horizontal ellipsis end style  

  1. begin mathsize 14px style horizontal ellipsis end style 

  2. begin mathsize 14px style horizontal ellipsis end style 

Jawaban:

Misalkan u equals x squared

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals cell 2 x end cell row cell integral fraction numerator d u over denominator d x end fraction space straight d x end cell equals cell integral 2 x space straight d x end cell row cell integral straight d u end cell equals cell integral 2 x space straight d x end cell end table

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral x cubed square root of 4 minus 2 x squared end root space d x end cell equals cell integral x squared square root of 4 minus 2 x squared end root open parentheses 1 half times 2 x space d x close parentheses end cell row blank equals cell 1 half integral u square root of 4 minus 2 u end root space d u end cell end table end style  

Misalkan p equals 4 minus 2 u rightwards arrow u equals 2 minus 1 half p

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight d p over denominator straight d u end fraction end cell equals cell negative 2 end cell row cell integral fraction numerator straight d p over denominator straight d u end fraction space straight d u end cell equals cell integral negative 2 straight d u end cell row cell integral straight d p end cell equals cell integral negative 2 straight d u end cell end table

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 half integral u square root of 4 minus 2 u end root space d u end cell row blank equals cell 1 half integral open parentheses 2 minus 1 half p close parentheses square root of p times open parentheses negative 1 half left parenthesis negative 2 right parenthesis d u close parentheses end cell row blank equals cell 1 half integral 2 p to the power of 1 half end exponent minus 1 half p to the power of 3 over 2 end exponent open parentheses negative 1 half d p close parentheses end cell row blank equals cell negative 1 fourth open square brackets open parentheses 2 times 2 over 3 times p to the power of 3 over 2 end exponent close parentheses minus open parentheses 1 half times 2 over 5 times p to the power of 5 over 2 end exponent close parentheses plus C close square brackets end cell row blank equals cell negative 1 fourth open square brackets 4 over 3 p to the power of 3 over 2 end exponent minus 1 fifth p to the power of 5 over 2 end exponent plus C close square brackets end cell row blank equals cell negative 1 third p to the power of 3 over 2 end exponent plus 1 over 20 p to the power of 5 over 2 end exponent plus C end cell end table end style  

Substitusikan bentuk p menjadi bentuk x kembali.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 1 third p square root of p plus 1 over 20 p squared square root of p plus C end cell row blank equals cell negative 1 third left parenthesis 4 minus 2 u right parenthesis to the power of 3 over 2 end exponent plus 1 over 20 left parenthesis 4 minus 2 u right parenthesis to the power of 5 over 2 end exponent plus C space end cell row blank equals cell negative 1 third open parentheses 4 minus 2 x squared close parentheses to the power of 3 over 2 end exponent plus 1 over 20 open parentheses 4 minus 2 x squared close parentheses to the power of 5 over 2 end exponent plus C end cell end table end style  

Jadi, nilai dari integral tersebut adalah Error converting from MathML to accessible text.

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