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Hitunglah nilai dari integral-integral tentu berikut ini.  c)

Pertanyaan

Hitunglah nilai dari integral-integral tentu berikut ini. 

c) begin mathsize 14px style integral subscript 2 superscript 3 open parentheses x minus 2 close parentheses space d x end style  

Pembahasan Soal:

Perlu diingat salah satu sifat integral tentu yaitu:

integral subscript m superscript n open square brackets f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis close square brackets straight d x equals integral subscript m superscript n f left parenthesis x right parenthesis straight d x minus integral subscript m superscript n g left parenthesis x right parenthesis straight d x

Berdasarkan sifat integral tertentu pada pengurangan fungsi maka:

 table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 2 superscript 3 open parentheses x minus 2 close parentheses space d x end cell equals cell integral subscript 2 superscript 3 x space straight d x minus integral subscript 2 superscript 3 2 space straight d x end cell row blank equals cell open square brackets fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 2 x close square brackets subscript 2 superscript 3 end cell row blank equals cell open square brackets 1 half x squared minus 2 x close square brackets subscript 2 superscript 3 end cell row blank equals cell open square brackets 1 half open parentheses 3 close parentheses squared minus 2 open parentheses 3 close parentheses close square brackets minus open square brackets 1 half open parentheses 2 close parentheses squared minus 2 open parentheses 2 close parentheses close square brackets end cell row blank equals cell open square brackets 1 half times 9 minus 6 close square brackets minus open square brackets 1 half times 4 minus 4 close square brackets end cell row blank equals cell open square brackets 9 over 2 minus 12 over 2 close square brackets minus open square brackets 2 minus 4 close square brackets end cell row blank equals cell open square brackets negative 3 over 2 close square brackets minus open square brackets negative 2 close square brackets end cell row blank equals cell negative 3 over 2 plus 4 over 2 end cell row blank equals cell 1 half end cell end table   

Dengan demikian, nilai dari begin mathsize 14px style integral subscript 2 superscript 3 open parentheses x minus 2 close parentheses space d x end style adalah begin mathsize 14px style 1 half end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 02 Agustus 2021

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