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Hasil dari integral open parentheses 3 x minus 2 close parentheses squared straight d x equals horizontal ellipsis

  1. x cubed minus 6 x squared plus 9 x plus c

  2. 2 x cubed minus 12 x squared plus 9 x plus c

  3. 2 x cubed minus 6 x squared plus 9 x plus c

  4. 3 x cubed minus 6 x squared minus 4 x plus c

  5. 3 x cubed minus 6 x squared plus 4 x plus c

Pembahasan Soal:

Ingatlah bahwa

undefined

dan

begin mathsize 14px style integral k space d x equals k x plus c end style.

Akibatnya

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

Jadi, jawaban yang tepat adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 03 Mei 2021

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Pertanyaan yang serupa

Integral dari  terhadap  adalah ....

Pembahasan Soal:

0

Roboguru

Tentukan hasil pengintegralan tak tentu dan tuliskan dalam bentuk akar tunggal.

Pembahasan Soal:

0

Roboguru

Pembahasan Soal:

Gunakan konsep integral tak tentu.

begin mathsize 14px style integral a x to the power of n space straight d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c end style 

Perhatikan perhitungan berikut.

begin mathsize 14px style integral open parentheses 2 x minus 3 close parentheses space straight d x equals fraction numerator 2 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 3 x plus c equals x squared minus 3 x plus c end style  

Jadi, diperoleh hasilnya adalah begin mathsize 14px style x squared minus 3 x plus c end style.

0

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Integral fungsi pada soal dapat dikerjakan dengan metode substitusi. Misalkan begin mathsize 14px style 2 x plus 9 equals p end style maka dengan menurunkan kedua ruas diperoleh begin mathsize 14px style 2 d x equals d p end style sehingga begin mathsize 14px style d x equals 1 half d p end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript blank square root of 2 x plus 9 end root d x end cell equals cell integral subscript blank left parenthesis 2 x plus 9 right parenthesis to the power of 1 half end exponent d x space end cell row blank equals cell integral subscript blank left parenthesis p right parenthesis to the power of 1 half end exponent times 1 half d p end cell row blank equals cell 1 half integral subscript blank left parenthesis p right parenthesis to the power of 1 half end exponent d p end cell row blank equals cell 1 half open parentheses fraction numerator 1 over denominator begin display style 1 half end style plus 1 end fraction p to the power of 1 half plus 1 end exponent close parentheses plus C end cell row blank equals cell 1 half open parentheses 2 over 3 p square root of p close parentheses plus C end cell end table end style       

dengan begin mathsize 14px style C end style konstanta. Selanjutnya dengan mensubstitusi kembali nilai undefined, diperoleh 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript blank square root of 2 x plus 9 end root d x end cell equals cell 1 half open parentheses 2 over 3 left parenthesis 2 x plus 9 right parenthesis square root of 2 x plus 9 end root close parentheses plus C end cell row blank equals cell 1 third left parenthesis 2 x plus 9 right parenthesis square root of 2 x plus 9 end root plus C end cell end table end style .


Jadi, jawaban yang benar adalah B.

1

Roboguru

Tentukan nilai

Pembahasan Soal:

begin mathsize 14px style integral fraction numerator x squared minus 4 x plus 10 over denominator x squared square root of x end fraction text d end text x end stylebegin mathsize 14px style equals integral fraction numerator x squared over denominator x squared square root of x end fraction d x minus integral fraction numerator 4 x over denominator x squared square root of x end fraction d x plus integral fraction numerator 10 over denominator x squared square root of x end fraction d x end style

                                  begin mathsize 14px style equals integral fraction numerator 1 over denominator square root of x end fraction d x minus 4 integral fraction numerator 1 over denominator x square root of x end fraction d x plus 10 integral fraction numerator 1 over denominator x squared square root of x end fraction d x equals integral fraction numerator 1 over denominator square root of x end fraction d x minus 4 integral fraction numerator 1 over denominator square root of x cubed end root end fraction d x plus 10 integral fraction numerator 1 over denominator square root of x to the power of 5 end root end fraction d x equals integral x to the power of negative 1 half end exponent d x minus 4 integral x to the power of negative 3 over 2 end exponent plus 10 integral x to the power of negative 5 over 2 end exponent d x end style

                                   size 14px equals fraction numerator size 14px 1 over denominator size 14px minus begin mathsize 14px display style 1 half end style size 14px plus size 14px 1 end fraction size 14px x to the power of size 14px minus size 14px 1 over size 14px 2 size 14px plus size 14px 1 end exponent size 14px minus fraction numerator 4 over denominator size 14px minus begin mathsize 14px display style 3 over 2 end style size 14px plus size 14px 1 end fraction size 14px x to the power of size 14px minus size 14px 3 over size 14px 2 size 14px plus size 14px 1 end exponent size 14px plus fraction numerator size 14px 10 over denominator size 14px minus begin mathsize 14px display style 5 over 2 end style size 14px plus size 14px 1 end fraction size 14px x to the power of size 14px minus size 14px 5 over size 14px 2 size 14px plus size 14px 1 end exponent size 14px plus size 14px C size 14px equals fraction numerator size 14px 1 over denominator begin mathsize 14px display style 1 half end style end fraction size 14px x to the power of size 14px 1 over size 14px 2 end exponent size 14px minus fraction numerator 4 over denominator begin mathsize 14px display style negative 1 half end style end fraction size 14px x to the power of size 14px minus size 14px 1 over size 14px 2 end exponent size 14px plus fraction numerator size 14px 10 over denominator begin mathsize 14px display style negative 3 over 2 end style end fraction size 14px x to the power of size 14px minus size 14px 3 over size 14px 2 end exponent size 14px plus size 14px C size 14px equals size 14px 2 size 14px x to the power of size 14px 1 over size 14px 2 end exponent size 14px minus size 14px 4 begin mathsize 14px style left parenthesis negative 2 right parenthesis end style size 14px x to the power of size 14px minus size 14px 1 over size 14px 2 end exponent size 14px plus size 14px 10 begin mathsize 14px style left parenthesis negative 2 over 3 right parenthesis end style size 14px x to the power of size 14px minus size 14px 3 over size 14px 2 end exponent size 14px plus size 14px C size 14px equals size 14px 2 square root of size 14px x size 14px plus fraction numerator size 14px 8 over denominator square root of size 14px x end fraction size 14px minus fraction numerator size 14px 20 over denominator size 14px 3 square root of size 14px x to the power of size 14px 3 end root end fraction size 14px plus size 14px C size 14px equals size 14px 2 square root of size 14px x size 14px plus fraction numerator size 14px 8 over denominator square root of size 14px x end fraction size 14px minus fraction numerator size 14px 20 over denominator size 14px 3 size 14px x square root of size 14px x end fraction size 14px plus size 14px C

                                  

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