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Pertanyaan

integral subscript 1 superscript 2 open parentheses 3 x squared plus 2 x minus 4 close parentheses straight d x = ...

Pembahasan Soal:

Perhatikan perhitungan berikut ini.

Ingat, integral:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses d x end cell equals cell integral f open parentheses x close parentheses d x plus-or-minus integral g open parentheses x close parentheses d x end cell row cell integral x to the power of n d x end cell equals cell fraction numerator 1 over denominator 1 plus n end fraction x to the power of n plus 1 end exponent plus C end cell row cell integral c d x end cell equals cell c x plus C end cell end table

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 1 superscript 2 open parentheses 3 x squared plus 2 x minus 4 close parentheses straight d x end cell equals cell open square brackets fraction numerator 3 x to the power of 2 plus 1 end exponent over denominator 1 plus 2 end fraction plus fraction numerator 2 x to the power of 1 plus 1 end exponent over denominator 1 plus 1 end fraction minus 4 x close square brackets subscript 1 superscript 2 end cell row blank equals cell open square brackets fraction numerator 3 x cubed over denominator 3 end fraction plus fraction numerator 2 x squared over denominator 2 end fraction minus 4 x close square brackets subscript 1 superscript 2 end cell row blank equals cell open square brackets x cubed plus x squared minus 4 x close square brackets subscript 1 superscript 2 end cell row blank equals cell open square brackets 2 cubed plus 2 squared minus 4 times 2 minus open parentheses 1 cubed plus 1 squared minus 4 times 1 close parentheses close square brackets end cell row blank equals cell open square brackets 8 plus 4 minus 8 minus open parentheses 1 plus 1 minus 4 close parentheses close square brackets end cell row blank equals cell open square brackets 4 plus 2 close square brackets end cell row blank equals 6 end table

Jadi, hasil dari integral subscript 1 superscript 2 open parentheses 3 x squared plus 2 x minus 4 close parentheses straight d x adalah 6.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Ayu

Mahasiswa/Alumni Universitas Negeri Padang

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

Diketahui , dan . Tentukan:

Pembahasan Soal:

0

Roboguru

Tentukanlah nilai integral di bawah ini: c.

Pembahasan Soal:

Ingat!

  table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses space d x end cell equals cell integral subscript a superscript b f open parentheses x close parentheses space d x plus-or-minus integral subscript a superscript b g open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b k f left parenthesis x right parenthesis space d x end cell equals cell k integral subscript a superscript b f left parenthesis x right parenthesis space d x end cell row cell integral subscript a superscript b a x to the power of n space d x end cell equals cell open parentheses fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent close parentheses subscript a superscript b space end cell end table 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 0 superscript 2 open parentheses x cubed minus 6 x squared plus 8 x close parentheses space d x end cell row blank equals cell integral subscript 0 superscript 2 x cubed space d x minus 6 integral subscript 0 superscript 2 x squared space d x plus 8 integral subscript 0 superscript 2 x space d x end cell row blank equals cell open parentheses fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent close parentheses subscript 0 superscript 2 minus 6 open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent close parentheses subscript 0 superscript 2 plus 8 open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent close parentheses subscript 0 superscript 2 end cell row blank equals cell 1 fourth open parentheses x to the power of 4 close parentheses subscript 0 superscript 2 minus 6 times 1 third open parentheses x cubed close parentheses subscript 0 superscript 2 plus 8 times 1 half open parentheses x squared close parentheses subscript 0 superscript 2 end cell row blank equals cell 1 fourth open parentheses x to the power of 4 close parentheses subscript 0 superscript 2 minus 2 open parentheses x cubed close parentheses subscript 0 superscript 2 plus 4 open parentheses x squared close parentheses subscript 0 superscript 2 end cell row blank equals cell 1 fourth open parentheses 2 to the power of 4 minus 0 to the power of 4 close parentheses minus 2 open parentheses 2 cubed minus 0 cubed close parentheses plus 4 open parentheses 2 squared minus 0 squared close parentheses end cell row blank equals cell 16 over 4 minus 16 plus 16 end cell row blank equals 4 end table  

Jadi, integral subscript 0 superscript 2 open parentheses x cubed minus 6 x squared plus 8 x close parentheses space d x equals 4.

0

Roboguru

Diketahui . Nilai  yang memenuhi adalah ...

Pembahasan Soal:

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b open parentheses f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses close parentheses space d x end cell equals cell integral subscript a superscript b f open parentheses x close parentheses space d x plus-or-minus integral subscript a superscript b g open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b k times f open parentheses x close parentheses space d x end cell equals cell k integral subscript a superscript b f open parentheses x close parentheses space d x end cell row cell integral subscript a superscript b a x to the power of n space d x end cell equals cell open square brackets fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent close square brackets subscript a superscript b end cell end table 

 

Diketahui integral subscript 1 superscript p open parentheses x minus 1 close parentheses squared space d x equals 2 2 over 3, maka tentukan nilai p.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 1 superscript p open parentheses x minus 1 close parentheses squared space d x end cell equals cell 2 2 over 3 end cell row cell integral subscript 1 superscript p open parentheses x squared minus 2 x plus 1 close parentheses space d x end cell equals cell 2 2 over 3 end cell row cell integral subscript 1 superscript p x squared space d x minus 2 integral subscript 1 superscript p x space d x plus integral subscript 1 superscript p 1 space d x end cell equals cell 2 2 over 3 end cell row cell 1 third open square brackets x cubed close square brackets subscript 1 superscript p minus open square brackets x squared close square brackets subscript 1 superscript p plus open square brackets x close square brackets subscript 1 superscript p end cell equals cell 2 2 over 3 end cell row cell 1 third open parentheses p cubed minus 1 close parentheses minus open parentheses p squared minus 1 close parentheses plus open parentheses p minus 1 close parentheses end cell equals cell 8 over 3 end cell row cell open parentheses p cubed minus 1 close parentheses minus 3 open parentheses p squared minus 1 close parentheses plus 3 open parentheses p minus 1 close parentheses end cell equals 8 row cell p cubed minus 3 p squared plus 3 p minus 9 end cell equals 0 end table 

Faktorkan polinom di atas.

table attributes columnalign right center left columnspacing 0px end attributes row cell p cubed minus 3 p squared plus 3 p minus 9 end cell equals 0 row cell open parentheses p minus 3 close parentheses open parentheses p squared plus 3 close parentheses end cell equals 0 row p equals cell 3 logical or p equals plus-or-minus square root of negative 3 end root end cell end table 

Nilai p yang mungkin adalah p equals 3.

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Nilai dari

Pembahasan Soal:

0

Roboguru

Nilai dari  adalah ...

Pembahasan Soal:

Ingat!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b open square brackets f left parenthesis x right parenthesis plus-or-minus g left parenthesis x right parenthesis close square brackets space d x end cell equals cell integral subscript a superscript b f left parenthesis x right parenthesis space d x plus-or-minus integral subscript a superscript b g left parenthesis x right parenthesis space d x end cell row cell integral subscript a superscript b k f left parenthesis x right parenthesis space d x end cell equals cell k integral subscript a superscript b f left parenthesis x right parenthesis space d x end cell end table end style 

Maka,

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 1 superscript 3 open parentheses 6 x squared minus 4 x plus 5 close parentheses space d x end cell row blank equals cell 6 integral subscript 1 superscript 3 x squared space d x minus 4 integral subscript 1 superscript 3 x space d x plus integral subscript 1 superscript 3 5 space d x end cell row blank equals cell 6 open square brackets 1 third x cubed close square brackets subscript 1 superscript 3 minus 4 open square brackets 1 half x squared close square brackets subscript 1 superscript 3 plus 5 open square brackets x close square brackets subscript 1 superscript 3 end cell row blank equals cell 2 open parentheses 3 cubed minus 1 cubed close parentheses minus 2 open parentheses 3 squared minus 1 squared close parentheses plus 5 open parentheses 3 minus 1 close parentheses end cell row blank equals cell 2 times 26 minus 2 times 8 plus 5 times 2 end cell row blank equals cell 52 minus 16 plus 10 end cell row blank equals 46 end table end style 

Sehingga, begin mathsize 14px style integral subscript 1 superscript 3 open parentheses 6 x squared minus 4 x plus 5 close parentheses space d x equals 46 end style.

Jadi, tidak ada jawaban yang tepat.

0

Roboguru

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