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Nilai dari

Nilai dari begin mathsize 14px style integral from 0 to 10 of open parentheses 3 x squared sin invisible function application 3 x close parentheses d x equals horizontal ellipsis end style 

  1. begin mathsize 14px style 50 1 over 9 square root of 3 plus 32 over 9 end style 

  2. begin mathsize 14px style 50 1 over 9 square root of 3 minus 32 over 9 end style 

  3. begin mathsize 14px style 25 1 over 9 square root of 3 minus 32 over 9 end style 

  4. begin mathsize 14px style 25 1 third square root of 3 plus 32 over 9 end style 

  5. begin mathsize 14px style 21 1 third square root of 3 plus 32 over 9 end style 

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S. Nur

Master Teacher

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Pembahasan

Karena fungsi yang akan diintegralkan terdiri dari bentuk aljabar dan bentuk trigonoemtri sin 3 x maka gunakan teknik integral parsial. Maka,

Karena fungsi yang akan diintegralkan terdiri dari bentuk aljabar begin mathsize 14px style left parenthesis 3 x squared right parenthesis end style dan bentuk trigonoemtri sin3x maka gunakan teknik integral parsial.

Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral from 0 to 10 of open parentheses 3 x squared sin invisible function application 3 x close parentheses d x end cell equals cell open square brackets 3 x squared open parentheses negative 1 third cos invisible function application 3 x close parentheses minus 6 x open parentheses 1 over 9 sin invisible function application 3 x close parentheses plus 6 open parentheses 1 over 27 cos invisible function application 3 x close parentheses close square brackets subscript 0 superscript 10 end cell row blank equals cell open square brackets negative x squared cos invisible function application 3 x minus fraction numerator 2 x over denominator 3 end fraction sin invisible function application 3 x plus 2 over 9 cos invisible function application 3 x close square brackets subscript 0 superscript 10 end cell row blank equals cell open parentheses open parentheses negative 10 close parentheses squared cos invisible function application 30 to the power of straight o minus fraction numerator 2 open parentheses 10 close parentheses over denominator 3 end fraction sin invisible function application 30 to the power of straight o plus 2 over 9 cos invisible function application 30 to the power of straight o close parentheses minus open parentheses 0 minus fraction numerator 2 open parentheses 0 close parentheses over denominator 3 end fraction sin invisible function application 0 to the power of straight o plus 2 over 9 cos invisible function application 0 to the power of straight o close parentheses end cell row blank equals cell open parentheses 100.1 half square root of 3 minus 20 over 3.1 half plus 2 over 9.1 half square root of 3 close parentheses minus open parentheses 0 minus 0 plus 2 over 9 close parentheses end cell row blank equals cell 50 square root of 3 minus 10 over 3 plus 1 over 9 square root of 3 minus 2 over 9 end cell row blank equals cell 50 1 over 9 square root of 3 minus 32 over 9 end cell end table end style 

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