Pertanyaan

Nilai dari ∫ ( 10 x 3 − 2 x 5 ) d x = ...

Nilai dari $\int (10 x^{3} - \frac{5}{2 x}) d x = ...$

$10 over 4 square root of x cubed end root plus fraction numerator 3 over denominator 4 square root of x cubed end root end fraction plus C$
$4 square root of x to the power of 5 end root minus fraction numerator 5 over denominator square root of x end fraction plus C$
$10 x cubed plus fraction numerator 3 over denominator 2 x end fraction plus C$

A. Armanda

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat! Maka, nilai dari adalah: Sehingga, . Jadi, jawaban yang tepat adalah E.

Ingat!

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral a x to the power of n space straight d x end cell equals cell fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent end cell row cell integral open parentheses f open parentheses x close parentheses plus-or-minus g open parentheses x close parentheses close parentheses space straight d x end cell equals cell integral f open parentheses x close parentheses space straight d x plus-or-minus integral g open parentheses x close parentheses space straight d x end cell row cell integral k times f open parentheses x close parentheses space straight d x end cell equals cell k integral f open parentheses x close parentheses space straight d x end cell end table$

Maka, nilai dari $integral open parentheses 10 square root of x cubed end root minus fraction numerator 5 over denominator 2 square root of x end fraction close parentheses space straight d x$ adalah:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses 10 square root of x cubed end root minus fraction numerator 5 over denominator 2 square root of x end fraction close parentheses space straight d x end cell row blank equals cell 10 integral square root of x cubed end root space straight d x minus 5 over 2 integral fraction numerator 1 over denominator square root of x end fraction space straight d x end cell row blank equals cell 10 integral x to the power of 3 over 2 end exponent space straight d x minus 5 over 2 integral x to the power of negative 1 half end exponent space straight d x end cell row blank equals cell 10 times fraction numerator 1 over denominator begin display style 3 over 2 end style plus 1 end fraction x to the power of 3 over 2 plus 1 end exponent minus 5 over 2 times fraction numerator 1 over denominator negative begin display style 1 half end style plus 1 end fraction x to the power of negative 1 half plus 1 end exponent plus C end cell row blank equals cell 10 times fraction numerator 1 over denominator begin display style bevelled 5 over 2 end style end fraction x to the power of 5 over 2 end exponent minus 5 over 2 times fraction numerator 1 over denominator begin display style bevelled 1 half end style end fraction x to the power of 1 half end exponent plus C end cell row blank equals cell 10 times 2 over 5 square root of x to the power of 5 end root minus 5 over 2 times 2 square root of x plus C end cell row blank equals cell 4 square root of x to the power of 5 end root minus 5 square root of x plus C end cell end table$

Sehingga, $table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 10 square root of x cubed end root minus fraction numerator 5 over denominator 2 square root of x end fraction close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x to the power of 5 end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table$ .

Jadi, jawaban yang tepat adalah E.