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Hasil dari  adalah ...

Pertanyaan

Hasil dariintegral open parentheses 2 over x minus 3 close parentheses squared space straight d x  adalah ...

  1. negative 4 x to the power of negative 1 end exponent minus 12 ln space x plus 9 x plus C  

  2. 4 x to the power of negative 1 end exponent minus 12 ln space x plus 9 x plus C   

  3. negative 4 x to the power of negative 1 end exponent minus 12 ln space x minus 9 x plus C  

  4. negative 4 x to the power of negative 1 end exponent plus 12 ln space x plus 9 x plus C   

  5. 4 x to the power of negative 1 end exponent minus 12 ln space x minus 9 x plus C   

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 2 over x minus 3 close parentheses squared space straight d x end cell equals cell integral open parentheses 4 over x squared minus 12 over x plus 9 close parentheses straight d x end cell row blank equals cell integral open parentheses 4 x to the power of negative 2 end exponent minus 12 over x plus 9 close parentheses straight d x end cell row blank equals cell negative 4 x to the power of negative 1 end exponent minus 12 ln space x plus 9 x plus C end cell end table

Jadi, jawaban yang tepat adalah A

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Roy

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 05 Juni 2021

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Pembahasan Soal:

Diketahui:

f apostrophe left parenthesis x right parenthesis equals 1 minus 2 x

begin mathsize 14px style f left parenthesis 3 right parenthesis equals 4 end style

Ditanya: f open parentheses x close parentheses?

Jawab: Untuk mencari nilai f open parentheses x close parentheses dari fungsi turunan maka kita harus mengintegralkan.

 table attributes columnalign right center left columnspacing 0px end attributes row cell integral f apostrophe open parentheses x close parentheses end cell equals cell integral open parentheses 1 minus 2 x close parentheses d x end cell row cell f open parentheses x close parentheses end cell equals cell x minus x squared plus C end cell end table

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 3 close parentheses end cell equals 4 row cell 3 minus 9 plus C end cell equals 4 row cell negative 6 plus C end cell equals 4 row C equals 10 end table end style

Substitusi nilai C:

f open parentheses x close parentheses equals negative x squared plus x plus 10

Oleh karena itu, jawaban yang tepat adalah D.
 

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Nilai dari

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 2 superscript 4 9 x squared minus x plus 2 space d x end cell equals cell open square brackets 1 third 9 x cubed minus 1 half x squared plus 2 x close square brackets subscript 2 superscript 4 end cell row blank equals cell open square brackets 3 x cubed minus 1 half x squared plus 2 x close square brackets subscript 2 superscript 4 end cell row blank equals cell open square brackets 3 open parentheses 4 close parentheses cubed minus 1 half open parentheses 4 close parentheses squared plus 2 open parentheses 4 close parentheses close square brackets minus open square brackets 3 open parentheses 2 close parentheses cubed minus 1 half open parentheses 2 close parentheses squared plus 2 open parentheses 2 close parentheses close square brackets end cell row blank equals cell open square brackets 3 open parentheses 64 close parentheses minus 1 half open parentheses 16 close parentheses plus 8 close square brackets minus open square brackets 3 open parentheses 8 close parentheses minus 1 half open parentheses 4 close parentheses plus 4 close square brackets end cell row blank equals cell 192 minus 22 end cell row blank equals 170 end table

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

Roboguru

Pembahasan Soal:

integral fraction numerator straight x squared plus 2 over denominator square root of straight x cubed plus 6 straight x plus 1 end root end fraction dx  Misalkan  straight u equals straight x cubed plus 6 straight x plus 1  maka  du equals 3 straight x squared plus 6 space dx  1 third du equals straight x squared plus 2 space dx  Sehingga  integral fraction numerator straight x squared plus 2 over denominator square root of straight x cubed plus 6 straight x plus 1 end root end fraction dx equals integral fraction numerator 1 over denominator square root of straight u end fraction.1 third dx  equals 1 third integral straight u to the power of negative 1 half end exponent du  equals 1 third fraction numerator straight u to the power of begin display style 1 half end style end exponent over denominator begin display style 1 half end style end fraction plus straight C  equals 2 over 3 square root of straight u plus straight C  equals 2 over 3 square root of straight x cubed plus 6 straight x plus 1 end root plus straight C

Roboguru

Selesaikan soal berikut dengan substitusi!

Pembahasan Soal:

Misalkan: , maka bentuk aljabar pada integral dapat dituliskan sebagai berikut

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral left parenthesis x to the power of 5 plus 3 right parenthesis to the power of 6 times x to the power of 4 d x end cell equals cell integral u to the power of 6 fraction numerator d u over denominator 5 end fraction end cell row blank equals cell 1 fifth integral u to the power of 6 d u end cell row blank equals cell 1 fifth left parenthesis 1 over 7 u to the power of 7 plus C right parenthesis end cell row blank equals cell u to the power of 7 over 35 plus C end cell row blank blank blank end table end style

Substitusikan pemisalan u, pada hasil integral

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell u to the power of 7 over 35 plus C end cell equals cell open parentheses x to the power of 5 plus 3 close parentheses to the power of 7 over 35 plus C end cell row blank equals cell 1 over 35 open parentheses x to the power of 5 plus 3 close parentheses to the power of 7 plus C end cell end table end style

Jadi, begin mathsize 14px style integral x to the power of 4 open parentheses x to the power of 5 plus 3 close parentheses to the power of 6 d x end styleError converting from MathML to accessible text..

Roboguru

Nilai dari

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript negative 1 end subscript superscript 2 open parentheses negative x squared plus 2 x minus 1 close parentheses d x end cell equals cell open square brackets negative 1 third x cubed plus x squared close square brackets subscript negative 1 end subscript superscript 2 end cell row blank equals cell open square brackets open parentheses negative 1 third open parentheses 2 close parentheses cubed plus open parentheses 2 close parentheses squared close parentheses minus open parentheses negative 1 third open parentheses negative 1 close parentheses cubed plus open parentheses negative 1 close parentheses squared close parentheses close square brackets end cell row blank equals cell open square brackets open parentheses negative 8 over 3 plus 4 close parentheses minus open parentheses 1 third plus 1 close parentheses close square brackets end cell row blank equals cell negative 9 over 3 plus 3 end cell row blank equals cell negative 3 plus 3 end cell row blank equals 0 end table

Jadi, Error converting from MathML to accessible text..

Oleh karena itu, jawaban yang benar adalah C.

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