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Pertanyaan

table attributes columnalign right center left columnspacing 0px end attributes row cell integral left parenthesis x cubed plus 8 x right parenthesis space d x end cell equals cell... end cell end table 

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral left parenthesis x cubed plus 8 x right parenthesis space d x end cell equals cell fraction numerator x to the power of 3 plus 1 end exponent over denominator 3 plus 1 end fraction plus fraction numerator 8 x to the power of 1 plus 1 end exponent over denominator 1 plus 1 end fraction plus C end cell row blank equals cell x to the power of 4 over 4 plus fraction numerator 8 x squared over denominator 2 end fraction plus C end cell row blank equals cell 1 fourth x to the power of 4 plus 4 x squared plus C end cell end table

Jadi. integral dari bentuk table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral left parenthesis x cubed plus 8 x right parenthesis space d x end cell end table adalah Error converting from MathML to accessible text. 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 05 Juni 2021

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Pertanyaan yang serupa

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral left parenthesis 4 x cubed minus 2 x squared plus 3 x minus 4 right parenthesis space d x end cell equals cell fraction numerator 4 over denominator 3 plus 1 end fraction x to the power of 4 minus fraction numerator 2 over denominator 2 plus 1 end fraction x cubed plus fraction numerator 3 over denominator 1 plus 1 end fraction x squared minus fraction numerator 4 over denominator 0 plus 1 end fraction x plus C end cell row blank equals cell x to the power of 4 minus 2 over 3 x cubed plus 3 over 2 x squared minus 4 x plus C end cell end table

1

Roboguru

=....

Pembahasan Soal:

Ingat, 

integral x to the power of n space end exponent d x equals fraction numerator 1 over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C integral 1 over x d x equals ln space x plus C

sehingga 

table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 6 x to the power of negative 11 end exponent minus 4 x to the power of negative 3 end exponent plus 6 x to the power of negative 1 end exponent close parentheses d x end cell equals cell negative 6 over 10 x to the power of negative 10 end exponent plus 4 over 2 x to the power of negative 2 end exponent plus 6 space ln space x plus C end cell row blank equals cell negative 3 over 5 x to the power of negative 10 end exponent plus 2 x to the power of negative 2 end exponent plus 6 space ln space x plus C end cell end table

 

0

Roboguru

Pembahasan Soal:

Ingat, 

integral subscript blank a x to the power of n 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 space comma space n not equal to negative 1 

Maka, 

integral open parentheses 1 half x to the power of 4 plus 1 third x cubed minus 1 close parentheses space straight d x equals fraction numerator 1 half over denominator 5 end fraction x to the power of 5 plus fraction numerator 1 third over denominator 4 end fraction x to the power of 4 minus x plus c space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 5 over 2 x to the power of 5 plus 4 over 3 x to the power of 4 minus x plus c  

Jadi, integral open parentheses 1 half x to the power of 4 plus 1 third x cubed minus 1 close parentheses space straight d x equals 5 over 2 x to the power of 5 plus 4 over 3 x to the power of 4 minus x plus c  .

 

0

Roboguru

Tentukan integral-integral tak tentu berikut ini. f)

Pembahasan Soal:

Integral tak tentu merupakan sebuah bentuk operas pengintegralan pada suatu fungsi menghasilkan suatu fungsi baru.

Nilai dari begin mathsize 14px style integral open parentheses 3 square root of x plus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 3 square root of x plus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end cell equals cell integral 3 square root of x space straight d x plus integral fraction numerator 2 over denominator square root of x end fraction space straight d x end cell row blank equals cell integral 3 x to the power of begin inline style 1 half end style end exponent space straight d x plus integral 2 x to the power of negative begin inline style 1 half end style end exponent space straight d x end cell row blank equals cell 3 integral x to the power of begin inline style 1 half end style end exponent space straight d x plus 2 integral x to the power of negative begin inline style 1 half end style end exponent space straight d x end cell row blank equals cell 3 open parentheses 2 over 3 x to the power of begin inline style 1 half end style plus 1 end exponent plus C close parentheses plus 2 open parentheses 2 x to the power of negative begin inline style 1 half end style plus 1 end exponent plus C close parentheses end cell row blank equals cell 2 x to the power of begin inline style 3 over 2 end style end exponent plus 4 x to the power of begin inline style 1 half end style end exponent plus C end cell row blank equals cell 2 x square root of x plus 4 square root of x plus C end cell row blank equals cell 2 square root of x open parentheses x plus 2 close parentheses plus C end cell end table end style          

Jadi, nilai dari begin mathsize 14px style integral open parentheses 3 square root of x plus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end style adalah begin mathsize 14px style 2 square root of x open parentheses x plus 2 close parentheses plus C end style.

0

Roboguru

Tentukan integral berikut ini.

Pembahasan Soal:

Perhatikan penyelesaian integral berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral left parenthesis 100 x to the power of 4 minus 60 x cubed plus 30 x squared minus 10 x plus 1 right parenthesis space d x end cell row blank equals cell 100 integral x to the power of 4 d x minus 60 integral x cubed d x plus 30 integral x squared d x minus 10 integral x d x plus integral 1 d x end cell row blank equals cell fraction numerator 100 over denominator 4 plus 1 end fraction x to the power of 4 plus 1 end exponent minus fraction numerator 60 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus fraction numerator 30 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 10 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus x plus C end cell row blank equals cell 100 over 5 x to the power of 5 minus 60 over 4 x to the power of 4 plus 30 over 3 x cubed minus 10 over 2 x squared plus x plus C end cell row blank equals cell 20 x to the power of 5 minus 15 x to the power of 4 plus 10 x cubed minus 5 x squared plus x plus C end cell end table end style 

Jadi, nilai dari integral fungsi tersebut adalah sebagai berikut.

Error converting from MathML to accessible text.

0

Roboguru

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