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Tentukan hasil dari begin mathsize 14px style integral x square root of x squared minus 6 end root space d x end style.

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Pembahasan Video:

Pembahasan Soal:

Untuk menyelesaikan integral dengan substitusi aljabar, soal harus diubah ke dalam bentuk begin mathsize 14px style integral u to the power of n space d u end style dengan begin mathsize 14px style u equals f left parenthesis x right parenthesis end style dan begin mathsize 14px style n not equal to 1 end style.

Diketahui integral dengan fungsi begin mathsize 14px style integral x square root of x squared minus 6 end root space d x end style.
Misal: begin mathsize 14px style u equals x squared minus 6 end style maka begin mathsize 14px style d u equals 2 x space d x end style.

Penyelesaian integral tersebut adalah  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral x square root of x squared minus 6 end root space d x end cell equals cell 1 half integral 2 x square root of u space d x end cell row blank equals cell 1 half integral left parenthesis u right parenthesis to the power of 1 half end exponent d u end cell row blank equals cell fraction numerator begin display style bevelled 1 half end style over denominator begin display style bevelled 1 half plus 1 end style end fraction u to the power of 1 half plus 1 end exponent plus C end cell row blank equals cell fraction numerator begin display style bevelled 1 half end style over denominator begin display style bevelled 3 over 2 end style end fraction left parenthesis x squared minus 6 right parenthesis to the power of 3 over 2 end exponent plus C end cell row blank equals cell 1 third left parenthesis x squared minus 6 right parenthesis square root of x squared minus 6 end root plus C end cell end table end style   

Jadi, hasil dari begin mathsize 14px style integral x square root of x squared minus 6 end root space d x end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third left parenthesis x squared minus 6 right parenthesis square root of x squared minus 6 end root plus end cell end table C end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 12 April 2021

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