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∫ − 2 1 ​ ( 2 x − 4 ) 2 d x ​ = = = = = = ​ ∫ − 2 1 ​ ( 2 x − 4 ) ( 2 x − 4 ) d x ∫ − 2 1 ​ ( 4 x 2 − 16 x + 16 ) d x [ 3 .... ​ x 3 − .... x 2 + .... x ] − 2 1 ​ { ( 3 4 ​ ... . 3 − 8... . 2 + 16.... ) − ( 3 4 ​ ( .... ) 3 − 8 ( .... ) 2 + 16 ( .... ) ) } ( .... − .... + .... ) − ( .... − .... + .... ) .... ​

 

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Y. Umi

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

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 begin mathsize 14px style integral subscript negative 2 end subscript superscript 1 open parentheses 2 x minus 4 close parentheses squared d x equals negative 4 over 3 end style.

Pembahasan

Integral Tentu Jadi, .

Integral Tentu

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript negative 2 end subscript superscript 1 open parentheses 2 x minus 4 close parentheses squared text dx end text end cell equals cell integral subscript negative 2 end subscript superscript 1 open parentheses 2 x minus 4 close parentheses open parentheses 2 x minus 4 close parentheses text dx end text end cell row blank equals cell integral subscript negative 2 end subscript superscript 1 open parentheses 4 x squared minus 16 x plus 16 close parentheses d text x end text end cell row blank equals cell open square brackets 4 over 3 x cubed minus 8 x squared plus 16 x close square brackets subscript negative 2 end subscript superscript 1 end cell row blank equals cell open curly brackets open parentheses 4 over 3 open parentheses 1 close parentheses cubed minus 8 open parentheses 1 close parentheses squared plus 16 open parentheses 1 close parentheses close parentheses minus open parentheses 4 over 3 open parentheses negative 2 close parentheses cubed minus 8 open parentheses negative 2 close parentheses squared plus 16 open parentheses negative 2 close parentheses close parentheses close curly brackets end cell row blank equals cell open parentheses 4 over 3 minus 8 plus 16 close parentheses minus open parentheses 32 over 3 minus open parentheses negative 32 close parentheses plus open parentheses negative 32 close parentheses close parentheses end cell row blank equals cell 4 over 3 minus 32 over 3 plus 8 end cell row blank equals cell negative 28 over 3 plus 24 over 3 end cell row blank equals cell negative 4 over 3 end cell end table end style

Jadi, begin mathsize 14px style integral subscript negative 2 end subscript superscript 1 open parentheses 2 x minus 4 close parentheses squared d x equals negative 4 over 3 end style.

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Lukiskan sketsa grafik y = x 15 ​ untuk domain 3 ≤ x ≤ 5 . Tunjukkan bahwa: 6 < ∫ 0 5 ​ x 15 ​ d x < 10 .

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