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Tentukan nilia integral dari  a.

Pertanyaan

Tentukan nilia integral dari 

a. integral open parentheses 8 x cubed minus 6 x squared plus 4 x minus 1 close parentheses d x equals..

Pembahasan Soal:

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

Nilai dari integral open parentheses 8 x cubed minus 6 x squared plus 4 x minus 1 close parentheses d x equals 2 x to the power of 4 minus 2 x cubed plus 2 x squared minus x plus C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Rahmawati

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 05 Juni 2021

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Carilah nilai  jika  dan !

Pembahasan Soal:

f apostrophe left parenthesis x right parenthesis adalah turunan dari f left parenthesis x right parenthesis. Maka gunakan integral untuk mencari f left parenthesis x right parenthesis. Cara pengerjaan integral tak tentu adalah integral straight a x to the power of straight n space d x equals fraction numerator a over denominator straight n plus 1 end fraction x to the power of straight n plus 1 end exponent plus C.


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


Diketahui bahwa f left parenthesis 0 right parenthesis equals 3. Maka untuk mencari nilai C, substitusikan f left parenthesis 0 right parenthesis equals 3 ke dalam fungsi f left parenthesis x right parenthesis.


table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 0 right parenthesis end cell equals 3 row cell 0 squared minus 0 plus C end cell equals 3 row C equals 3 end table


Jadi nilai f left parenthesis x right parenthesis equals x squared minus x minus 3.

0

Roboguru

Tentukan hasil dari integral berikut: a.

Pembahasan Soal:

Perhatikan rumus integral berikut

integral a to the power of x d x equals fraction numerator a to the power of x over denominator ln open parentheses a close parentheses end fraction plus C

Dengan menggunakan rumus di atas diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell integral 1 over 4 to the power of negative x minus 1 end exponent d x end cell equals cell integral 4 to the power of x plus 1 end exponent d x end cell row blank equals cell integral open parentheses 4 to the power of x times 4 close parentheses space d x end cell row blank equals cell 4 integral 4 to the power of x d x end cell row blank equals cell 4 times open parentheses fraction numerator 4 to the power of x over denominator ln open parentheses 4 close parentheses end fraction close parentheses plus C end cell row blank equals cell fraction numerator 4 to the power of x times 4 over denominator ln open parentheses 4 close parentheses end fraction plus C end cell row blank equals cell fraction numerator 4 to the power of x plus 1 end exponent over denominator ln open parentheses 4 close parentheses end fraction plus C end cell end table

Dengan demikian hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 4 to the power of negative x minus 1 end exponent end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 to the power of x plus 1 end exponent over denominator ln open parentheses 4 close parentheses end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table.

0

Roboguru

Tentukan integral tak tentu berikut ini!

Pembahasan Soal:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses x squared plus 1 close parentheses squared over x squared d x end cell row blank equals cell integral open parentheses fraction numerator x to the power of 4 plus 2 x squared plus 1 over denominator x squared end fraction close parentheses d x end cell row blank equals cell integral open parentheses x to the power of 4 over x squared plus fraction numerator 2 x squared over denominator x squared end fraction plus 1 over x squared close parentheses d x end cell row blank equals cell integral open parentheses x squared plus 2 plus x to the power of negative 2 end exponent close parentheses d x end cell row blank equals cell fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus fraction numerator 2 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent plus fraction numerator 1 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent plus C end cell row blank equals cell 1 third x cubed plus 2 over 1 x to the power of 1 plus fraction numerator 1 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus C end cell row blank equals cell 1 third x cubed plus 2 x minus x to the power of negative 1 end exponent plus C end cell row blank equals cell 1 third x cubed plus 2 x minus 1 over x plus C end cell end table end style 

Jadi, hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x squared plus 1 close parentheses squared over x squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table end style adalah Error converting from MathML to accessible text.    

 

0

Roboguru

Pembahasan Soal:

Ingat bahwa:

  • integral a straight d x equals a x plus C 

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell integral thin space 3 straight d x end cell equals cell 3 x end cell row blank equals cell 3 x plus C end cell end table 

Jadi, y equals integral thin space 3 straight d x equals 3 x plus C.

0

Roboguru

Bila , maka  adalah ....

Pembahasan Soal:

Dengan menerapkan rumus integral tak tentu, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral space f open parentheses x close parentheses space d x end cell equals cell integral space x to the power of 2 n end exponent space d x end cell row blank equals cell fraction numerator 1 over denominator 2 n plus 1 end fraction x to the power of 2 n plus 1 end exponent plus c end cell end table end style 

Dengan demikian, hasil begin mathsize 14px style integral space f open parentheses x close parentheses space d x end style adalah begin mathsize 14px style fraction numerator 1 over denominator 2 n plus 1 end fraction x to the power of 2 n plus 1 end exponent plus c end style.

Jadi, jawaban yang tepat adalah E.

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