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Tentukan integral 3 over 2 x to the power of 2 over 3 end exponent space d x equals...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral 3 over 2 x to the power of 2 over 3 end exponent end cell equals cell fraction numerator 1 over denominator begin display style 2 over 3 end style plus 1 end fraction x to the power of 2 over 3 plus 1 end exponent plus C end cell row blank equals cell fraction numerator 1 over denominator begin display style 5 over 3 end style end fraction times 3 over 2 x to the power of 5 over 3 end exponent plus C end cell row blank equals cell 3 over 5 times 3 over 2 cube root of x to the power of 5 end root plus C end cell row blank equals cell 9 over 10 cube root of x to the power of 5 end root plus C end cell row blank equals cell 9 over 10 x cube root of x squared end root plus C end cell end table

Jadi, integral 3 over 2 x to the power of 2 over 3 end exponent space d x equals 9 over 10 x cube root of x squared end root plus C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Herlanda

Mahasiswa/Alumni STKIP PGRI Jombang

Terakhir diupdate 06 Juni 2021

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Integral atau anti turunan memenuhi algoritma berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px integral subscript size 14px a superscript size 14px b k x to the power of n size 14px d size 14px x end cell size 14px equals cell right enclose fraction numerator size 14px k size 14px x to the power of size 14px n size 14px minus size 14px 1 end exponent over denominator size 14px n size 14px minus size 14px 1 end fraction end enclose subscript size 14px a superscript size 14px b end cell row blank size 14px equals cell fraction numerator size 14px k size 14px b to the power of size 14px n size 14px minus size 14px 1 end exponent over denominator size 14px n size 14px minus size 14px 1 end fraction size 14px minus fraction numerator size 14px k size 14px a to the power of size 14px n size 14px minus size 14px 1 end exponent over denominator size 14px n size 14px minus size 14px 1 end fraction end cell end table

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript 3 open parentheses 3 x squared plus 2 x plus 1 close parentheses d x end cell equals 25 row cell right enclose 3 over 3 x cubed plus 2 over 2 x squared plus x end enclose subscript a superscript 3 end cell equals 25 row cell open parentheses 3 cubed plus 3 squared plus 3 close parentheses minus open parentheses a cubed plus a squared plus a close parentheses end cell equals 25 row cell 39 minus open parentheses a cubed plus a squared plus a close parentheses end cell equals 25 row cell open parentheses a cubed plus a squared plus a close parentheses end cell equals 14 row a equals 2 row blank rightwards arrow cell 3 a equals 3 cross times 2 end cell row blank equals 6 row blank blank blank end table end style

Jadi nilai dari begin mathsize 14px style 3 a equals 6 end style.

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Diketahui . Nilai dari  adalah ....

Pembahasan Soal:

Integral atau anti turunan memenuhi algoritma berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px integral subscript size 14px a superscript size 14px b k x to the power of n size 14px d size 14px x end cell size 14px equals cell right enclose fraction numerator size 14px k size 14px x to the power of size 14px n size 14px minus size 14px 1 end exponent over denominator size 14px n size 14px minus size 14px 1 end fraction end enclose subscript size 14px a superscript size 14px b end cell row blank size 14px equals cell fraction numerator size 14px k size 14px b to the power of size 14px n size 14px minus size 14px 1 end exponent over denominator size 14px n size 14px minus size 14px 1 end fraction size 14px minus fraction numerator size 14px k size 14px a to the power of size 14px n size 14px minus size 14px 1 end exponent over denominator size 14px n size 14px minus size 14px 1 end fraction end cell end table

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript 3 open parentheses 3 x squared plus 2 x plus 1 close parentheses d x end cell equals 25 row cell right enclose 3 over 3 x cubed plus 2 over 2 x squared plus x end enclose subscript a superscript 3 end cell equals 25 row cell open parentheses 3 cubed plus 3 squared plus 3 close parentheses minus open parentheses a cubed plus a squared plus a close parentheses end cell equals 25 row cell 39 minus open parentheses a cubed plus a squared plus a close parentheses end cell equals 25 row cell open parentheses a cubed plus a squared plus a close parentheses end cell equals 14 row a equals 2 row blank rightwards arrow cell 3 a equals 3 cross times 2 end cell row blank equals 6 row blank blank blank end table end style

Jadi nilai dari begin mathsize 14px style 3 a equals 6 end style.

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Antiturunan  adalah...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell F left parenthesis x right parenthesis end cell equals cell fraction numerator 6 x squared over denominator 2 end fraction minus 2 x plus C end cell row blank equals cell 3 x squared minus 2 x plus C end cell end table end style

Jadi, jawaban yang tepat adalah C

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Hasil dari  adalah ...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral 2 over 3 square root of x d x end cell equals cell integral 2 over 3 x to the power of 1 half end exponent d x end cell row blank equals cell 2 over 3 times fraction numerator 1 over denominator begin display style 1 half end style plus 1 end fraction x to the power of 1 half plus 1 end exponent plus C end cell row blank equals cell 2 over 3 times fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction times x to the power of 3 over 2 end exponent plus C end cell row blank equals cell 2 over 3 times 2 over 3 times x to the power of 3 over 2 end exponent end cell row blank equals cell 4 over 9 x to the power of 3 over 2 end exponent plus C end cell row blank equals cell 4 over 9 times x times x to the power of 1 half end exponent plus C end cell row blank equals cell 4 over 9 x square root of x plus C end cell end table  

Dengan demikian, jawaban yang tepat adalah D.

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